From the Steam desktop client, in the lower-left hand corner, there is a link that reads:
+ ADD A GAME...
Clicking this link presents you with an option to Add a Non-Steam Game.
You can select from a list, or browse to any executable file on your hard drive.
Additional note (contributed by Asunez)
Doing this only adds the program to your local Steam library. Logging onto the same account on another computer will not restore Non-Steam games to the list. Also there is no Steam Cloud backup, and no support for community sites. If the game is online multiplayer, all Steam invite-theme operations will not work, either (no joining servers, no inviting friends, no party/lobby).
All Non-Steam games are somewhat impaired, and while you can save screenshots, and others can see you are playing the game, it is not the same as purchasing the same title on Steam.
It's basically adding a shortcut to a program, and making Steam overlay work in that Non-Steam game.