1) Remove seats from car and take them apart. Test fit the seat covers by sliding them on. The very best results will be achieved if the seat covers have to be stretched to go on. If the seat covers appear even slightly loose or baggy, take the whole works to a reputable shop and have the seat covers altered and installed there. Broken springs or dry-rotted cushions will also require expert attention. Extra hint: showing up at the shop with disassembled seats rather than the entire antique car could save substantial $$ because the job will appear more defined and manageable. Your car will also not be exposed to accidental nicks in the shop or the hazards of being left out at night.
2) I do not like to install seat covers over old, hard vinyl. If this is what you have, cut the hog rings and remove the old seat covers before test fitting as in 1). If the new seat covers fit tight enough, I would recommend removing the old seat covers in all cases.
3) If you do plan to install the new seat covers over the old, cut the piping off of the old seat covers with a razor blade. 4) The disposable hog ring pliers which are often found are borderline unusable. Unfortunately, with a standard markup, a good set could cost over $40 from a shop. An alternative would be to offer to borrow a set for $10 plus leave a $30 refundable deposit.
5) The seating areas of the seat covers (places where you actually touch - not the seat's sides or back of the backrests) will come in a combination of pleated material and flat vinyl "panels". The pleated material has about 3/8" of foam embossed to the back of it but the panels have no foam. This can lead to a permanent sort of thin air pocket in the panels adjacent to the pleats. I prevent this problem by taking a piece foam-backed headliner material (used on all cars 1978-up) and doubling it over with contact cement. I then attach a piece of this doubled-over foam to the back of each of the "panels" by gluing it just around the edges with contact cement. This way, the entire seating area of the seat cover will have about 3/8" of foam backing and will lie flat.
6) I always contact cement the cushion seat covers into place and I usually cement the backrest covers into place as well. This is particularly important if the seat is contoured in any way and the seat cover has no listings to make it conform to the contours. I feel that this keeps the seat cover from stretching out of shape and will therefore appear newer for a longer time period. This step may be skipped if the new seat covers fit perfectly tight and have listings where needed. It is also a moot point if the new seat covers are going directly over cotton rather than foam rubber or old seat covers. This is about all I have to say. If someone runs into a problem, just take it to a shop. With much of the work already done, it should not cost too much to have any difficulties taken care of at a shop.