The real answer to your question is by the adoption of the convoy system, in 1917, which did two things: by concentrating the number of ships at sea, it also denuded the rest of the ocean of possible targets, making it far less likely that a submarine would stumble across a target by chance; and by surrounding the convoys with escorts, it meant that any submarine that wished to attack enemy shipping had to put herself at risk of counter attack to do so. But I read your question as more a query about forms of anti-submarine warfare, so let's look more closely at that.

Anti-submarine warfare has two components: detection and destruction.

Before the war many attempts were made to effect the destruction of submarine boats, several of them holding out fair promise of success, but problem of detection remained unsolved. Gunfire, ramming, "lasso nets," explosive creeps and sweeps and rudimentary depth charges were all useless if the target could not be located; even if by some good fortune a submarine was caught on the surface or her periscope was sighted, it was unlikely in the extreme that she would still be visible at the moment an attack was delivered. The boats' invisibility shielded them from attack as effectively as it concealed their own acts of aggression.

The first attempts to detect submarines took three forms. Most obviously, a strict look-out could be kept from surface ships by the 'Mark I eyeballs' of men trained to recognise periscopes and conning towers. If successful this method did at least hold out the promise that patrol craft, scouts and destroyers could force the submarine to remain submerged where her speed and vision were seriously impaired, and harass her until a body of larger ships had passed out of range. The disadvantages were twofold: rapid exhaustion of the watching crew, and a high proportion of time consuming false alarms caused by everything from shadows and sticks to whales.

A more promising method of surface observation was provided by the indicator net, a simple mesh designed to wrap itself around a submarine and carry away from its moorings, allowing patrol vessels to attack the intruder by following the movement of buoys. Indicator nets were laid abundantly during the war, most notably in the Dover Barrage.

The second method, echo-sounding and its related techniques, was not widely understood before 1914, although methods of underwater sound signalling were developed and active interest in underwater acoustics had better existed since at least 1800. The third, observation from the air, was regarded and numerous attempts were made to spot submerged submarines from balloons, airships and aeroplanes from the late 1890s - a use of one radical innovation to combat another that represents an intriguing triumph of imagination over naval conservatism. Early aircraft nevertheless laboured under the twin disadvantages of low endurance and designs that hindered the observer's downward field of vision. With the exception of airships they also lacked the ability to carry the sort of bombs needed to disable a submarine boat.

When - if -a submarine was detected, there were also three ways in which she could be actively attacked: collision (ramming), explosives either fired or dropped (guns, bombs, depth charges) and towed explosives (sweeps or trawls). Although apparently less likely to reap success, weapons of opportunity such as the gun or depth charge proved to be more effective than the sweeps that were favoured before 1914. This was because they narrowed the gap between detection and attempted destruction. Sweeps tended to be used after a sighting to hunt a whole area - they were operated 'blind' and it is unsurprising that they accounted for only two German boats in the war. The passive obstructions used - nets and mines – were effective precisely because they depended less on (in theory) be left in situ for long periods. Actually the fierce currents and adverse weather conditions of the in the North Sea reduced their effectiveness, but they were nevertheless vital in the anti-submarine war.

The actual destruction of a submarine was not necessarily the main aim of ASW. As well as preventing an attack by keeping the submarine under water and away from its main targets, the defending surface forces could score a victory simply by damaging the boat. It was recognised that the submarine was highly vulnerable and anything other than minor leaks were very dangerous because seawater would either sink the craft by destroying her buoyancy or generate chlorine gas by coming into contact with battery acid.

Even so, the difficulties encountered in anti-submarine warfare were evidently great. The usual solution to new problems in naval warfare setting like against like - was far from obviously viable. The torpedo boat had been met by the destroyer, and one aircraft could fight another, but submarine v. submarine warfare was a desperate business in which the hunter could quickly become hunted and both combatants laboured under equal disadvantages. To be safe, a submarine boat on AS patrol had to be submerged, where her field of vision was restricted to what could be seen through a periscope raised a few inches above the surface, sometimes only for seconds at a time. Her target was small, manoeuvrable and acutely aware of the tactics and possibilities of submarine attack, and restrictions on underwater speed and endurance often made it impossible for a would-be assailant to get into an attacking position. In wartime the British found that only 8.1% of the torpedoes fired by one boat at another found their target, although the moral effect of such patrols in terms of forcing greater vigilance and caution from the enemy was great.

It was the weaknesses of the submarine rather than the strengths of her attackers that counted in World War I. Underwater craft were far slower than most of their prey and vulnerable on the surface, particularly in poor light when a boat was more likely to be caught unawares. Manoeuvres indicated, and experience proved, that it was difficult for a boat to hit a fast-moving target with torpedoes - but she could hardly remain on the surface to fight. If enough patrol craft were available, if the conditions were favourable and the waters restricted or shallow, and the target's position approximately known, it was even possible to keep a sub down until her batteries were exhausted and the air so foul that she had to surface. But that was very rare. From 1914-1918, it proved far, far easier to neutralise a submarine than to destroy her.

The First World War saw massive advances in the RN's ability to detect and destroy submarines. It went from using towed explosives and hand-thrown 'lance bombs' to using several sophisticated methods, involving a combination of aircraft, submarines, hydrophones (passive sonar), electro-magnetic methods, and depth charges. The RN was aided in this by the primitive nature of the submarines it faced - rather than being true submarines, spending the majority of their time submerged, they were more submersible torpedo boats, submerging only to stalk a target, and spending most of their time on the surface. The RN's tactics for attacking submarines can be separated into five main areas: self-defence of merchant ships, attacking U-boat bases (attack at source), attacking them while they were travelling between their bases and targets (attack in transit), attacking them in their patrol areas (hunting), or attacking them at their target (convoy).

At the start of the war, the only way the RN could detect and destroy submerged submarines was by using towed sweeps. These had been developed from the sweeps used in minesweeping, and worked in a very similar matter. A float was streamed from a towing ship, with charges placed on the tow cable. The sweep used by the RN at the start of WWI was called the 'Modified Single Sweep'. This carried a payload of nine 80lb charges, and could cover an area 300 yards long by 48 feet deep, using two wires. Should any wire be fouled, then an electrical signal was generated, giving the operator the go-ahead to fire the charges. RN planning for ASW warfare had concentrated on the protection of the battlefleet, rather than protection of trade. As such, sweeps were to be supplemented by the use of high speed and frequent course changes. These would prevent submarines from being able to move into a firing position, as the battlefleet could outrun any submarine, either submerged or surfaced. Mines were to be used to protect against attacks on harbours. Ramming was also used against submarine targets, especially those near the surface - Dreadnought's only kill during the war was U-29, ramming her on 18 March 1915. However, the war exposed major flaws in this. The sweep was only useful against very close targets, and provided little ability for the detection of targets. Several committees were set up to work on new methods to detect and destroy submarines. The first was the Submarine Committee (succeeded in 1916 by the Anti-Submarine Division (ASD)), followed in July 1915 by the Admiralty Board of Invention and Research. These committees explored a bewildering array of possibilities, from the frivolous to the serious. In the former category came suggestions like those of Admiral Fredrick Inglefield. He had, in the area under his command, placed teams of swimmers aboard motor launches - should the launch spot a sub periscope, the swimmers were to approach it stealthily, place a black bag over it, and smash it with a hammer. He had also attempted to train seagulls to crap on periscopes, to limited success. Somewhat more serious were the seagull proposals of Thomas Mills, who proposed to train seagulls to associate sub periscopes with food (trials were carried out with HMS B3, but to no avail). The most successful were the developments of the hydrophone and the depth charge. The hydrophone was, in the RN, the brainchild of Commander C P Ryan, who in peacetime had worked for the Marconi company. He was given official support early in 1915, along with the drifter Tarlair for use in trials. He quickly produced a non-directional hydrophone. In February 1915, a chain of these was set up along the British coast, with detectors set with spacings of ~1.5 miles, at depths between 50 and 100 fathoms. Following this successful deployment, they began to be deployed on ships, as the PGS (Portable General Service) set. In 1916, a directional hydrophone was produced by Ryan's establishment at Hawkcraig, with it entering service in 1917. However, in that year, the USN would enter the war. The USN had several much more effective hydrophone designs, which the RN would adopt. All hydrophones would suffer from the same limitations. The noise of flowing water prevented their use on ships moving at speed. This was also discouraged because the hydrophone could easily pick up the ship's own machinery noise. This meant that hunters had to 'sprint and drift', listening at low speed before making a high-speed run to the target. However, submarines could exploit this behaviour, drifting while the hunter drifted and moving while it sprinted. Even so, hydrophones were common, and were even deployed aboard seaplanes and blimps. Several other methods were taken seriously - several electromagnetic methods were deployed. Loops that detected the magnetic signature of subs were common, especially in fixed positions for harbour defence. A system that could detect submarines by the electric potential produced by the propeller was trialled, but did not enter service. An apparatus that detected currents between two or more towed electrodes and a sub entered service as the Search Apparatus Marks III, IV and V. It had an effective range of 100ft, and was considered the best short-range detector available.

The depth charge, meanwhile, came from the RN's Torpedo School at HMS Vernon (also responsible for mines). On the 7th December 1914, Jellicoe requested an ASW mine. As an expedient measure, several Mk II mines were converted into 'cruiser mines', detonated by a static line at a 45ft depth. The next big development was the Type C charge, a converted 65 lb bomb designed as an ASW bomb for aircraft. This had both a hydrostatic fuse and a contact fuse. However, this would be quickly superseded by the Type D charge, which had a 300lb Amatol charge, and a hydrostatic fuse. Ordered in August 1915, it entered service in January 1916, alongside a smaller 120lb version designed for slower craft. At first, these were just rolled from tracks on the stern of a ship, or slid off the side. From 1917, several bomb throwers, including modified Army howitzers, entered service. These could throw bombs or depth charges out to considerable ranges. The hydrophone and depth charge combination was highly effective. However, depth charges were used relatively sparingly during the war, rather than in the lavish patterns seen in WWII.

Tactics

The first main tactic was to defend merchants directly, by arming or camouflaging them. In February 1915, fifty 12pdr guns were allocated to the most vulnerable coastal vessels, with more guns following as they became available. By May 1915, 115 ships were armed with another 24 in the process of arming. That April, it had also been decided that one 4.7in gun would be mounted on the larger merchants engaged in overseas trade. As not enough guns were available at first, ships travelling outbound would transfer their guns to homeward-bound ships outside the danger area. These guns were considered highly valuable by merchant skippers, to the point where many would mount dummy guns. One ship so armed, the SS Nicosian, managed to bluff an attacking U-boat for long enough for rescue to arrive. Dazzle camouflage was also tried, whereby a ship was painted with geometric patterns that made her course difficult to determine. This was effective at keeping up morale and confusing surface sailors, but as shown here, was ineffective against submariners, who used the ship's masts and funnels to determine its course. Merchant skippers were also trained to zig-zag. It was hoped that the zig-zag would prevent an attacking sub getting a torpedo solution, forcing it to surface to use her gun, and giving the merchant a chance to fire back.

Attack at source was tricky to do throughout much of the war. The strength of the German High Seas Fleet precluded any attempt to attack the U-boat bases, especially those in Germany itself. However, U-boats based in Flanders could be targeted. Throughout the war, the RN's Dover Patrol bombarded their main bases, at Zeebrugge and Ostend. Air attacks were also made by the Royal Naval Air Service (RNAS), forcing the Germans to build concrete submarine pens. In early 1918, raids were made against both ports. These sought to scuttle blockships in the canals that led inland to Bruges, where the subs had moved. The raids had limited success - while blockships were scuttled in the canals, they failed to block them permanently. At the war's end, the USN was building up an air force to make strikes against U-boat bases and yards. The RNAS, had unfortunately been absorbed into the RAF, and so it's not clear how much the British would support this effort, as the RAF was much less interested in naval matters.