It's usually not a good idea to install ceramic tile directly over a vinyl floor, because vinyl is not solid enough to ensure an immobile base for the tile. In most cases, you'll want to install a layer of cement board over the vinyl and then tile over that. However, you can go directly over vinyl in certain circumstances--if it's a small space in a dry room (not a bathroom), and the vinyl is thick and solid and doesn't have any "give'' to the surface.
Load your belt sander with 80-grit sandpaper. Sand the vinyl floor, starting in one corner of the room and working across the floor. Run the sander forward and back in overlapping rows, moving on when the gloss or shine is gone from the floor. Thoroughly vacuum the dust.
Stretch your chalk snap line across the floor, from the middle of one wall to the middle of the wall across from it, dividing the room in two. If the string lines up with the seams of the vinyl tiles, then move the string a few inches over so it doesn't. Snap the line.
Stretch the snap line in the other direction, perpendicular to the first line, intersecting it at the middle. Again, make sure the string isn't lined up with the seams of the vinyl tiles. Lay a square at the intersection and square the string to the first line. Snap the line.
Spread thin set mortar over the intersection, using your notched trowel and covering several square feet. Press four floor tiles in place at the four corners of the intersection. Put spacers between them. Build out from there, spreading mortar and laying tiles. Use a tile cutter to trim to tiles at the ends so they fit against the walls.
Allow the mortar to dry overnight. Remove all the spacers. Spread grout over the tile with your grout float, squeezing it into the spaces between the tiles while scraping it off the surface. Use a damp sponge to wipe off the excess grout. Let it set for two days.
Vinyl floor installed before the 1980s may contain asbestos, and you never should sand it. If you think your floor could contain asbestos, contact your local health department about getting it tested. Wear a dust mask when sanding the floor. Wear eye protection when cutting the tiles.