Windows NT calls applied for enumerating processes:
CloseHandle
EnumProcesses
EnumProcessModules
GetModuleBaseName
GetModuleFileNameEx
OpenProcess

Windows 98/Me needs a different set of calls
CloseHandle
CreateToolhelp32Snapshot
Process32First
Process32Next

FoxPro code samples:

Terminating all running applications from a VFP program
http://www.news2news.com/vfp/?example=243

Enumerating Processes -- Win9*
http://www.news2news.com/vfp/?example=164

Enumerating Processes -- WinNT
http://www.news2news.com/vfp/?example=162

There are several ways of terminating a process. You might send WM_QUIT message to the window associated with a process. This works not every time, and even more reliable way is sending WM_SYSCOMMAND message with S_CLOSE parameter.

Sometimes none of these helps, so you have a last resort -- a heavy bombardment -- TerminateProcess API function. This function is a kind of destructive one, an application terminated may leave some files open, system resources not properly released etc.