Types  
    The depth charge is the most primitive dedicated ASW weapon. Even more primitive, but not dedicated, are only ramming and gunning if the enemy is on the surface; both variants of submarine "hunting" were exercised at all times but were the only options available to a stunned Royal Navy in the first three years of World War I.  

    It was an extraordinarily crude weapon - basically just a can filled with explosives and a hydrostatic fuze measuring the pressure of water around the weapon and detonating it at a certain, pre-set depth. It was an okay weapon for WWI - any attack would require the enemy to have been close to the surface, so he could be seen, and the depths to which submarines might dive were not great. The Royal Navy introduced the new weapon in 1916 and scored the first success with it on December 13th, 1916, against UB-29, a German submarine. Two depth charges had sufficed for her destruction, and indeed, the numbers dropped for each kill in WWI gave a serious underappreciation of what the Navy would need to drop in the future.  

    Two month after that success, and even before the U.S. entered the war, the USN began to develop a depth charge of their own, which was too weak to be successful. However, after the U.S. entry, the Royal Navy provided an example of their depth charges, which the U.S. fitted with a hydrostatic fuze of their own. 

The final U.S. WWI depth charge could detonate at up to 300ft depth and carried 300lbs explosives.    During the inter-war years, there was little effort for better depth charges, but the 600lbs variant was adopted for stern racks because of its better chance of success; the 300lbs variants were retained for the projectors.      WW2 started for the ASW department with essentially the same weapon it had ended WWI with, and development concentrated on increasing the depth in which a submarine might be successfully attacked; coupled with that, the sinking speed of the depth charges had to be increased.          The Mk 9 became the main variant. This was teardrop-shaped, capable of detonating at 1000ft, and entered service in 1943.

Mk 6 type depth charges and a K-gun aboard a U.S.  ASW patrol craft in 1942.

    Depth charges were abandoned by the U.S. Navy not much after World War II, the Navy preferring torpedos and ahead thrown proximity & contact weapons. Helicopters were the last U.S. weapons platform to retain depth charges, and many brown-water navies continue to use the depth charge today, in lieu of the hardly effective homing torpedos (since their sonar has problems distinguishing the bottom of shallow waters from a potential target).  

Useage 
The standard method of deploying a depth charge was by running it down a rail on the aft end of a ship. Different depth charges would be set a different depths, so a nice pattern would result and the submarine would, hopefully, end up in pieces. 

This was a useful strategy in WWI, but a submarine could evade this if it had already dived some time before. A more widespread pattern was needed to catch such a target. The obvious solution to this problem was throwing the depth charges far to the side, so as to create a sort of depth charge carpet. For this purpose, the Y-gun was created.          This was a projector, firing depth charges using a small explosive charge, located on the centerline of a ship and having two "exits", forming a Y. On each exit, a depth charge was tied, to be fired off in support of the other charges, and landing some hundreds of yards outboard.       This was an effective addition to the ASW forces, with one major flaw: it could only be mounted on the centerline, a location were traditionally little room is available.           Accordingly, a split version of the Y-gun, the K-gun, was developed - it could be mounted on the sides of the superstructure, firing one depth charge outboard.       Several of these could be and were mounted on each destroyer. They were the fleet destroyers' main and most effective ASW weapon, as those didn't receive Hegehog.

A K-gun. Note the short stump to the right of the projector's main arm, into which the explosive charges were loaded.