Wine isn't a standalone program and doesn't really "run" on it's own. It allows you to install and run Windows-based programs. To run a windows program, simply open up a terminal, cd into the folder containing the .exe file you wish to run, and type "wine program.exe". That should start up the program, assuming wine supports it.
Remember, Wine is still under development, and it can't handle every Windows program yet. Some programs will have buggy operation, and others might not run at all.
If the program requires installation on Windows, then it will also require installation under wine as well. Just run the install.exe and go through the installation procedure as you would under windows.
The command "winecfg" will bring up a graphic configuration tool for changing some wine settings. "wine uninstaller" will bring up an uninstallation tool.
Your installation might have entries set up in the main menu for some of these commands and installed programs (those that would have an entry under the Windows start menu). This depends on how the distro set up the wine package however.
For more information, read the manual page ("man wine"), and/or check out the documentation on the winehq