There's a million ways to accomplish this, however, we need a bit more specification to determine the best method.
If you're only looking at trying to launch Program A by clicking an icon, then a batch file is the simple solution. Remember to use the "Start" command to launch the programs, so the batch file doesnt wait for the first one to finish, before it launches the second program.
i.e.
start "C:\Program Files\Microsoft Office\Office\Winword.exe"
start "C:\Program Files\Windows Media Player\wmplayer.exe"
You can even do this to Start Menu links, web URL's, dang near anything you can double-click in windows...
i.e.
start "C:\Documents and Settings\All Users\Start Menu\Programs\Games\Thief - Deadly Shadows\Play Thief.lnk"
start "C:\Documents and Settings\All Users\Start Menu\Programs\Games\Thief - Deadly Shadows\Thief Trainer.lnk"
I do this for situations like GTA and the GTA Monitor program. When I click my *new* GTA button, it will kill any previous GTA Monitor thats running on my 2nd computer, launch GTA Monitor on my 2nd computer, then launch GTA on my local computer.
It waits until GTA has exited on my local computer (simply by not launching GTA with the Start command) , then it kills GTA Monitor on my 2nd PC, Clean and neat.
Just let me know what you're trying to accomplish and I'll paste some batch code I've written pertaining to that area.