Vinyl tiles: scrape the substrate and the back of the tiles as well as possible. A little sanding the back of the tiles to get as much of the old residue as you can.
Contact cement. Lightly paint the back of the tile and then the substrate( lightly, just a fine film) let those sit for approx. 10 minutes and then stick the tile, making positive you have it exactly where you want it before you touch the two adhesive coated surfaces together.

Ceramic: Remove the thinset on the substrate, along with any surrounding grout. Use cement mortar, not premixed mastic and mix up some mud. Set your tiles spacing it and pushing down to get the air out. If the tile sits low, you need more mud under the tile. If the tile sits high, push down and squeeze the excess thinset out of the grout joints and use a popsicle stick to remove the thinset in the joints. A wet sponge to wipe any thinset mess, with a bucket of water or a sink close by to wring the sponge out often. Let it sit for a day.

Next day scrape any thinset you missed out of the edges of the grout joints, vacuum, and then wipe down with a wet sponge. Mix your grout and let it sit.

%-10 minutes, remix the grout and get your grout floats and start packing the joints. Let that sit for about 10-15 minutes and using a clean wrung out sponge, wipe down and form the grout lines and remove excess grout from the tile surface. Let it sit for another 14-20 minutes

Using clean water and the sponge well wrung out each time. Wipe the tiles down in one direction, one swipe. Flip the sponge over and go right back over that swath. Rinse and wring out the sponge and do another swipe the same way. Wait about 10-15 minutes and do that same thing again.

Let it dry for about 5-10 minutes and then take a dry clean towel and buff off any haze left on the tiles. Kinda like waxing a car, and removing the wax.

AustinFloorguy

Thanks for the detailed instructions!!!