Stability Issues

• The major concern with laying tile over vinyl is that the vinyl won't provide a solid, immobile backing that will prevent any movement of the tile. If the substrate under the tile moves downward at all after it's installed, the grout and possibly the tiles themselves will crack. If the vinyl has padding under it, you'll have to strip it. If it's unpadded, walk over the vinyl with bare feet looking for any "give'' in the surface. Hammer in a few shank nails anywhere it moves, then see if it still moves. Make sure the vinyl is firmly attached throughout the room, with no air pockets anywhere.
  
  

Adhesion Issues

• Vinyl flooring is often glossy and shiny. This exactly the wrong surface to attempt to mount tiles, because the tile adhesive could slip off it. If there's any gloss on the tile--or even just shiny grime from years of polishing--it will have to come off before you can tile. The easiest way to do this is with a belt sander loaded with 80-grit sandpaper; just start at one wall and do every inch of the floor. If you can look at the floor from a few different angles and not see any brightly reflected light, you're good to go. (Caution: If your vinyl floors are about 20 years old or older, they may contain asbestos, and shouldn't be sanded. If you think there's any chance of the presence of asbestos, take a sample of the vinyl to your local health department for testing.)
  
  

Installation Issues

• Once the vinyl is stabilized and solid, you can lay the tiles like any other floor, with a few caveats. Go with tiles that are thick (1/2 inch is good) and relatively small (say, 6 inches across or less) to provide added strength. Use adhesive tile glue instead of mortar, spreading it down with a notched trowel. Lay out the tiles from the center of the room as usual, making the cuts at the edges of the room as needed. Grout according to the instructions on the grout packaging, making sure to seal the grout at the end against moisture.