You do not say what type of sub-floor you have, but if it is concrete, scrape off the vinyl, ( you can purchase a floor scraper from a local hardware store, such as Home Depot), then lay the tile directly over the concrete.
If you have a wooden subfloor, it should be at least 1/2 inch thick plywood, but 3/4 inch is the best way to go.
Apply a concrete leveling mix by spreading it over the plywood sub-floor. This serves three purposes. 1) It will level the floor out and 2), it will create a surface which will provide a good bond between the floor and the thinset mortar mix. 3) It will seal the subfloor.
If your sub-floor is wooden and not in good condition, it would be best to tear it up and replace with 3/4 " plywood.
If it is in good condition, but not thick enough, then I would do as freedom1st suggested and lay backer board or better still, (since it is going on the floor), would lay concrete board. It is sturdier.