What's the difference between a cruiser, a destroyer, a frigate, and a littoral combat ship?

This is meant to be a general overview of each of these ships and their capabilities, not looking at specific information such as size and armament (which can easily be found online, if you want specific facts about each ship). 

Littoral Combat Ship (LCS): One of the newest types of ships, made up of the Freedom and Independence Classes with only 3 ships in service. LCS's are very small, versatile ships that were created with the aim of extending the Navy's capabilities closer to the shore. LCS's are made to operate in shallower water than most USN platforms and have different modules that can be swapped in and out depending on the mission requirements. 

Cruiser (CG): Cruisers are now becoming less and less relevant, with only 22 left in the Ticonderoga-Class. Their main focus is to provide the Navy with a multi-functional guided missile platform (launching weapons systems such as the Tomahawk and other missiles via the ship's vertical launching system (VLS)) that can engage surface and air targets, as well as conduct anti submarine missions (SSW, surface ship warfare; AAW, anti-aircraft warfare; and ASW, anti-submarine warfare). 

Destroyer (DDG): One of the most central and important roles in the surface navy. The Navy currently has 62 destroyers in the Arleigh Burke Class, with plans for a new Zumwalt Class. Slightly smaller than cruisers, they can conduct a variety of missions, including ASW (anti-submarine warfare), AAW (anti-aircraft warfare) ASUW (anti-surface warfare) and are meant to be a multi-role surface platform with the capability to protect a strike group or naval force of any impending threats or targets. 

Frigate (FFG): There are only 22 frigates left in the Oliver Hazard Perry Class, with these ships intended to be replaced by the new LCS's. Frigates were designed mainly as a cost effective and relatively inexpensive escort platform that could protect merchants convoys, supply ships, as well as expeditionary and amphibious forces. They are smaller than destroyers and do not have the same degree of missile-launching capability.