I'm building up a fixed gear from a 1970's apollo and am replacing the cottered cranks. It looks as though I will be installing an entirely new drive-train and was wondering how I go about measuring for a bottom bracket. Could I just bring the old one into a shop or will I need to bring the frame itself?

You can measure the shell width yourself. This will tell you if it's english or italian (it's 99% likely that it's english). 68 = english, 70 = italian <- 99.9% of the time. At that point you choose the crankset and it'll tell you what LENGTH you need to acheive a some standard chainline figure.

And away you go.