I've had the car tuned up. Plugs, points, wires and I was told that the Accelerator something or other was in need of replacment and that it may be advised to replace.
I'm just guessing, of course, but it sounds like what they were telling you is that the accelerator pump is funky. That's a part of the carb that gives you a shot of fuel when you goose the throttle. Fixing that is covered in the book Steve references.
Fixing it is preferable to just replacing the whole thing because the parts place will try to sell you a rebuilt one anyway. There are some pretty horrible stories around about how badly those "rebuilt" or "remanufactured" parts work. I haven't heard of many people who were happy with them. It seems that the guys who get Cliff's book and do it themselves are pretty happy with the results. He explains things pretty well and it's well illustrated.
Keep in mind that your average tuneup guy will recommend replacement over rebuilding it because it's less hassle for him to just get a rebuilt one and stick it on the car and send you out the door. It's quicker than actually working on the one you have.