Once Launchy has been started, it hides in the background. You bring it forward by holding the alt key (apple on Mac, and ctrl on Linux) and tapping the space key. You can then type in a few keys of the program you are searching for and hit enter once it has been found. You can also make Launchy dissappear again by hitting escape or alt+space.
The official documentation (Readme.pdf) is distributed with the program
For further support, please see The Launchy Forums.