Running programs is not all that different from Windows. All you need to do is run "wine program.exe", making sure you are in the directory holding it, or else by entering the full path to it. If the program needs installation before you can use it, you just have to run the setup program first, "wine programsetup.exe" or whatever it's called and install it as you usually would.
Once you get it running in cli, you can easily create a shortcut or menu launcher for it in your gui. Just enter the same line in the "command" space of the shortcut properties that you used in the console. Exactly how to create a shortcut will depend on your window manager though.
Remember though that wine is still only in beta, and many programs won't work right, or at all. Most simple programs should be pretty stable, but more complicated or newer stuff might not work. Check out the wineapp database on their webpage to see what other people have gotten running and how.
As you no doubt read in the documentation, some programs will not run with the builtin setup, and may require original Windows .dll files. You can set these up, as well as other configuration options such as drives, by running "winecfg" (it's a gui app).
One thing that can help you figure out problems is, before you run any programs, to type "export WINEDEBUG=+loaddll" into the terminal. Then your terminal will show what .dll files your program is trying to load. If it fails to work, it'll probably be because of the last .dll file listed in the loadup sequence. Those are the dll's you should try running the native versions of.