Track deviation and low altitude alert in mountainous terrain followed the clearance to fly a published missed approach that had not been briefed in advance by the Cessna 750 flight crew.

Narrative

I was the Pilot Flying; going into ASE. Only my second time ever into ASE and unfamiliar with the approach. We briefed our options before takeoff if the weather deteriorated in ASE. When we got the ATIS the ceilings were reported to be 5;000 FT broken and 3;000 FT scattered. No precipitation and 6 miles of visibility. Decided to fly the VOR/DME into ASE. We briefed fly the approach and if at ALLIX we didn't see the airfield; we were going to go missed approach. Captain told me that our missed approach would be with the Tower; therefore; I never briefed the published missed. We went missed at ALLIX and the Controller gave us 'fly the published missed approach.' Since I did not brief it is unfamiliar and flew through the LOC course and ATC said they had a low altitude alert. We were at 14;000 FT which is the missed approach altitude and then I got back on course. ATC issued a climb 16;000 and no other issues. Brief the whole approach including the missed approach; all the time; every time; no matter what!