2001 Pontiac Sunfire Broken Lug nut and stem

I assume you sheered off the wheel stud also. The wheel stud can be drilled or banged out. If you drill be sure to drill a smaller hole through center of the stud and try to bang it out with a steel drift or center punch. Sometimes they just bang out easy.
The new stud is pressed into the hub - opposite of the way it came out. It can be installed by fitting it in the hub and tightening down a new lug nut to "pull" the new stud into the hub.A few large washers may be necessary to get the stud seated as you tighten the nut.
It is not a very complex fix but you must have patience -- and know this -- it happens all the time -- don't panic. Putting a little anti-sieze on the lug studs will prevent this from happening again.