You gotta know your SHIS! :P
First you will need to determine the type of headset you require. It may be integrated,zero stack, External cup,as well as threaded or threadless.
After having this information the measurements you will require are Inside Diameter of the head tube top and bottom. This measurement allows you to determine what type of fork you need, whether 1-1/8" , 1-1/4" or tapered from 1-1/8" to 1.5".
The measurement of the steer tube Outer Diameter on the fork, top (stem clamp 1-1/8" or 1") and the bottom OD (Crown Race Seat Diameter). Bearing seat and angle will also be needed if it is a threadless headset. You can usually just look at the old bearing to get this information if the side marking are still readable.
Cane Creek and Park Tools website both have a plethora of information regarding it. This poster from cane creek may help clarify.
See the larger version here
Cane Creek's wording:
The system addresses the critical interface dimensions required to fit a fork to a frame, as well as bearing location/cup type. To determine fit, four dimensions are needed: (1) stem-clamp diameter of fork, (2) crown-race seat diameter of fork, (3) head-tube top inside diameter, and (4) head-tube bottom inside diameter. Bearing location and cup-type are identified as (a) external cup (EC), (b) semi-integrated or ZeroStack (ZS), or (c) integrated (IS).