In general, the amphibious tanks of WWII used flotation devices and propellers to make their way into the beach, rather than driving along the seabed. Development of amphibious tanks in Britain started in WWI - on the 11th November 1918, a Mark IX tank fitted with air-filled flotation tanks was floated on Hendon Reservoir, as a proof of concept. However, the concept was dropped in the interwar period, thanks to a lack of investment and interest. During the 1930s, there was some interest in light amphibious tanks; these were mainly intended as reconnaissance vehicles, with the amphibious capability allowing them to cross rivers and canals. Several prototypes were tried, but none were found to be satisfactory. There were also some experiments in attaching floats to tanks. A Mark II light tank was fitted with a pair of pontoons and an outboard motor. This was used in a number of exercises, but as it took too long to fit or remove the floats, the idea was dropped.

During WWII, there was little development of amphibious tanks until after the catastrophe at Dieppe. Dieppe showed the need for tanks to be deployed alongside the troops on the beachhead. However, this could not easily be done by traditional landing craft; small tank landing craft could not be built in sufficient numbers, while larger craft were too much of a target, and if one was lost, a significant portion of the landing's tank strength would be lost with it. The amphibious tank promised to solve this problem. At first, the pontoon system was resurrected, and tried on the Crusader tank, but was again found to be unsuitable. It was replaced by a system developed by Nicholas Straussler, a Hungarian engineer who had moved to Britain, and who had designed many of the floats used in earlier trials. Straussler designed a canvas screen that would surround a tank and keep it afloat. It was light, compact, and easily collapsible, solving all the problems of the pontoon system. It was first tried on a Tetrarch light tank, which proved the idea to be a good one. It was then put into initial production with the Valentine infantry tank, which was in the process of being replaced with Churchill, Sherman and Cromwell tanks. To make it amphibious, the Valentine's hull was waterproofed, and it was given a propeller, driven from the tank's main engine. The resulting system was known as the Duplex Drive, or DD tank. It entered service with 27th Armoured Brigade from April 1943. The Brigade began training on Fritton Decoy, a lake on the Suffolk estate of Lord Somerleyton. Here, the crews practised launching from landing craft (using simulators constructed from Bailey Bridge components), escaping from sinking tanks, and manoeuvring on water. Once the initial training had been completed, training moved to Loch Fyne for sea training using real LCTs. Finally, the unit moved to Stokes Bay, on the Solent, for training in mass use of amphibious tanks. While the brigade was training, work was being carried out in converting the Sherman to the DD role. The Sherman was found to be much more suitable than the Valentine. The DD Valentine had low freeboard, and had to traverse its gun to the rear with the screen raised. The Sherman had a high freeboard and a low centre of gravity, making it much more seaworthy than the Valentine, and it could keep its gun facing forward, allowing it to engage targets as soon as it came ashore. Along with the three armoured regiments (equivalent to a US battalion) of the 27th Brigade, the DD tank was used by the 15th/19th Hussars and Nottinghamshire Yeomanry of the British Army, the 1st Hussars and Fort Garry Horse of the Canadian Army, and the 70th, 741st and 743rd Tank Battalions of the US Army.

If you mean submersible tanks that crawled upon the bottom of the ocean, that would be a definite no. I've done a fair amount of reading on the subject of unusual weapons of war, and submersible tanks are something that rarely even makes it to the drawing board (and considering some of the other things that at least made it that far, that's saying something). To my knowledge, neither the US nor any of the other Allied Powers have ever even attempted to develop such a thing. Maybe it simply never occurred to them, but more likely it was dismissed as impractical while it was still little more than an idea.

The Nazi war machine, on the other hand, was not so easily dissuaded by such petty concerns as practicality, and made several attempts at tanks that were fully submersible. The most successful were the Tauchpanzer (literally "dipping tank") variants of the Panzer III and Panzer IV, which had disposable waterproof coverings that could be remotely removed without leaving the vehicle as well as being equipped with bilge pumps and long, flexible snorkels allowing them to travel under up to 15 feet of water. Unfortunately, or rather, fortunately, the operation for which they'd been developed (Operation Sea Lion, a planned invasion of England via the English Channel) ended up being canceled due to unrelated concerns, and the two hundred or so units commissioned ended up just being used as normal tanks, only getting to show off their special abilities in a very small handful of river crossings.

A rather more eccentric Nazi submersible tank which never saw action (having been designed too near the end of the war) but purportedly preformed well in tests was the Seeteufel ("sea devil", the German name for the monkfish), which was actually a smallish U-Boat with tank treads that let it crawl up on land. It isn't entirely clear what purpose the Seeteufel would have served in combat had the war lasted long enough for it to be mass produced and deployed.