First, you need to separate strategy and tactics. Strategy is what occurs across multiple states and theaters. It is the general goals and methods employed by the belligerents. Tactics is what happens in battles when generals employ new technologies or move troops around. There is also some amorphous space between the two where stratagems are translated to tactics. It has a specific name but I don’t remember it.

Your question suggests you are angling more towards battlefield tactics, the development of skirmish warfare and siege techniques which both changed a great deal during the war. But the answer to STRATEGY is that the Northern plan did not fundamentally change during the war. General Winfield Scott, leader of American forces in the Mexican American War, created a plan known as the “Anaconda Strategy” which the Union followed throughout the war. There has been a ton written about it, Google that phrase and you’ll get a great deal of information. Basically the plan called for the Union to encircle the Confederacy by raising a naval blockade and taking control of the Mississippi River. Once that was done the Confederacy would be systematically cut to pieces while their economy was ground to dust. More or less that is how events played out despite several Union general’s best attempts to bumble it.

I’ll leave the changes in tactics to others better versed in them, but I would encourage you to look at changes in skirmishing, sieges, and the early developments in total/industrial war employed by Grant, Sheridan, Sherman, and others. There is a lively debate about whether the ACW was a total war or not and it heavily revolves around the late war implementation of scorched earth tactics employed by the late war Union as part of the plan to grind down the Southern economy.

You heard correctly about submarines. They were a tactical gambit employed by the South because the Union blockade was hurting the Confederacy badly. They were few in number and did not manage to affect the course of the war. The CSS Hunley was the first submarine to successfully destroy a warship when it sank the USS Housatonic. The Confederacy also employed a type of very low freeboard torpedo ram called a David Boat that was very similar to a submarine. They sat very low in the water as a defense and rammed targets with an explosive charge on the end of a long pole.

First off, the Confederate States did build one submarine, the hand-powered CSS Hunley, in an attempt to break the blockade of the Republican (Northern) US Navy. The Hunley did not work very well. It sank three times and killed three separate crews. The first two times, it sank in water shallow enough, that the Confederates were able to salvage her and use her again. The Hunley is credited with being the first submarine that actually sank an enemy warship, sinking the USS Houstiantic with a spar torpedo. However, the Hunley did not return from that attack. In 1995, Clive Cussler became fascinated with the Hunley and started a comprehensive search for its wreckage. It was found in 2000, was raised and a meticulous restoration of the Hunley has been on going at the former US Navy base in Charleston SC. You can learn more details and see photos at http://www.reddit.com/r/Warshipporn/ Use their search function for CSS Hunley to see four posts about this Civil War submarine.
As for your main question. When the war started, 74 year old Winfield Scott was still the commander of the US Army. His Grand Strategy for defeating the Confederate States included establishing a close blockade of Southern ports, a drive down the Mississippi river to split the confederacy in two, and a drive up the Tennessee river valley to Chattanoga TN, where a drive to Savanah GA could be launched, followed by a march through the Carolinas and an attack on Richmond VA, from the South. The North did not have a navy big enough to implement this plan right away, and Lincoln did not like the fact Scott told him it would take three years or more for this plan to work. Scott also told the president that a frontal attack on Richmond would not work and said it would be akin to trying to knock down a brick wall by banging your head against it. Winfield Scott was forced to retire on November 1st 1861. Scott was 74 years old at the time, was overweight, suffered from gout and afflicted with rheumatism. He was in no shape to hold a field command, but he did live long enough to see the Confederacy crushed. After wasting 1861, 1862 and 1863 trying to capture Richmond, in 1864, Lincoln belatedly decided to follow Scott's grand strategy, which had been derided in 1861 as the Anaconda Plan.
Source: "A Country Made by War: the Military History of the United States" by Geoffrey Perret.

I think Herman Hattaway and Archer Jones have argued that one big development in the north was the restoration, in the form of Sherman's march, of the strategic raid as a form of warfare. The basic idea -- moving into hostile territory that could not be held in the long term to inflict destruction and economic damage -- had been common in Western warfare prior to about the Peace of Westphalia, but it had fallen out of use somewhat.

However, the Hattaway/Jones view, I believe, is that this change in northern strategy, although a noteworthy development in military history terms, was ultimately not decisive in the war's outcome, because the north was already on the verge of victory for other reasons (basically, they think the south had a fairly weak sense of nationalism).

In addition to other comments you should consider that this war was the first one to use railroads and telegraphs to a large extent. Napoleon had set up some sort of semaphore system in France but the telegraph was far more extensive in the ACW and of course it was faster yet. This made it possible ofr Lincoln and theatre commanders like Grant to send messages to troops far away. The only big change was that by 1864 Grant was able to coordinate about 5 armies at once on the Virginia theatre including Butler's advance on Petersburg, Stonemans raid and another raid into VA, and Hunters move down the Valley. So finally we begin to see a commander able to coordinate many armies on a broad front.

The RRs allowed for much larger concentrations of troops. In the War of 1812 American armies barely numbered over 20,000 now they routinely approached 75 or 80,000 sometimes more. The RR also allowed for quicker concentrations of troops to defend threatened areas but it didnt always work perfectly.

Examples of this: in 1861, first battle of Bull Run saw joe johnson slip away from Anderson in the Valley and bring his troops over to win that battle. Also in 1862 Bragg managed to concentrate and redeploy several confederate armies using RR in the Kentucky invasion. In 1863 Chickamauga saw another confederate concentration that succeeded when they brought Longstreet's corps all the way from VA to GA. The union also managed to rail in reinforcements to Chattanooga in 1863.

You should definitely study these campaigns and the use of RRs. Also Lee's plan for the defense of So Carolina in 1861 called a centralized concentration that relied on the ability to rush to a threatened point rather than trying to defend every beach or port.