It depends on which of the downloads you got.
The prepackaged versions of the game—the ones labeled "Windows" or "Mac"—should just work once you unzip the zip file and run the program inside.
The ".love file" version of the game, however, contains a .love file that needs to be opened in this separate program.
In general, though, you shouldn't have to do much to run the game. If you could tell me more about what happens when you try to run the game, that may help me figure out what the problem is.