Re-finishing a vinyl and linoleum floor correctly is not something you want to do unless you have experience doing those types of floors. It's something a lot like carpet cleaning. A lot of people say they can do it, but it truly takes a long time to do it correctly. It would be difficult for me to write down all the steps one would need to take in order to do it properly without actually looking at the floor. If the wax/sealer is not to old and is not yellowing or has 1/4 inch thick of old wax on it then you can often just give it a light scrub and re-coat it.
You can also rent a highspeed buffer at most rental shop's and often combine that with a light coat of wax or sealer and pop it back into shape.
This of course is just my humble opinion. I've seen a lot of people start something that they wish they had not in trying to do this type of work without some specific experiance doing it. Good Luck
