I have a one-car attached garage. The wall on the house side of the garage is finished with siding (the other walls are unfinished). If I want to finish the house side wall, should I tear off the siding and replace with drywall or should I build a 2x4 frame next to the old wall and drywall over that?

Sounds like this was a later additon to the home, that's why there is siding showing. What are your plans for the other 2 walls? A 2x4 framing is not necessary, you can tear off the sliding and drywall. Once the siding is off you may find sheeting rather than just studs, leve the sheeting in place.

Thanks; we suspect that the garage was at one time a carport and was later framed in. What sort of sheathing might be present under the siding --something like Celotex board? If we tear off the siding, we'd probably want to check on the insulation in that wall (it seems cold in the winter), so the sheathing would have to come down too... should that be replaced or could we just go back over the with drywall?

If you remove the siding you could finf celotex or even plywood. If this is your opportunity to increase insulation remove just one small section of sheeting so you can see if there is room or a need for more insulation. Tell us the depth of the wall cavity once you get that far. Old insulation can be left in place keeping the vapor barrier againist your inisde wall. If you add insulation it must be unfaced with no new vapor barrier. I would cover that wall with Tyvec or and good wind stopping material before drywalling.