To list the processes you're running in the current terminal, type "ps".
Figure out which processes from the list you want to kill and select the process IDs (PIDs).
PID TTY TIME CMD
22452 pts/16 00:00:00 bash
18595 pts/16 00:00:00 vim
18596 pts/16 00:00:00 vim
20490 pts/16 00:00:00 ps
wnguyen@europa:~$ kill -9 18595 18596
That will kill off both vim processes. Type ps again to make sure they're dead.