The headset standard is determined by the inner diameter of the headtube. 30.2mm = 1", 34mm = 1-1/8", 37mm = 1-1/4". Since the standards are about 3mm apart you don't need to measure with a precision instrument.

If the inside of the tube is basically a plain cylindrical tube it uses a standard type of headset, or there are cup like areas machined in the ends that's for an integrated or "hidden" headset, but you'll have to go to the LBS to know which type fits.

You buy the fork to match the headset diameter, and need a steerer long enough for the length of the headtube, plus the height of the headset for a threaded headset, and add the height of the stem and any spacers you plan on using for a threadless headset.

There are more details involved in actually fitting the headset, and given your inexperience, you'll probably need help doing so, either from a knowledgeable fellow rider or the LBS, but at least this is a guide to what you have and will need.