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...if I already have a frame from the early 80's, I usually install a headset, which is pretty easy for that time period since centerpull brakes are mostly a memory , and it doesn't require a hanger. I then measure the fork width and rear dropouts, in order to select the proper hubs with regard to width. Check the frame and fork alignment. This is the time to consider spreading the rear and realigning the dropouts if youi want a 130 spacing and have a 126 frame.

I then either build wheels for it or find some in the reconditioned pile that have the proper width hubs. If it's a road bike I generally go with 700c wheel rims, especially in the 80's when that had pretty much become standard on the higher end stuff. When I have the wheels, I check the derailleur hanger for alignment (and correct it if required).

the rest of it is figuring which crank I have available, the spindle it requires in this frame, installing it, calculating gearing and possibly swapping out chainrings and cog numbers on the rear, measuring the frame for TT length and selecting the proper length stem, and whichever bar seems appropriate for the intended use. Saddle, seat post (measure for proper diameter)...I'm probably forgetting stuff. If I have a matched groupset, I generally use it.

If I already have brakes and levers that match the group, I use them with new pads. If not, measure reach with wheels installed front and rear, and look for something with dual pivots and the proper reach...usually ends up being from Tektro, but some others come in pretty close in price when they are on sale. I try to use components that work as well as the best stuff from the time period...dual pivot side pulls work even better than most of the early 80's single pivots. But those work pretty well too.