2002 Buick won't stay running

My car will not stay running unless you press on the gas and then wants to stall at every stop or sometimes when I have to brake. It has been doing this on and off for a couple of days and seems fine once you are running at higher speeds and seems to mostly stop acting up after the cars is ran for 5-10 miles.

Remove the Idle Air Control (IAC) and clean/inspect. Also check for vacuum leaks on all hose & fittings.