do i have to put any thing down on the painted floor FIRST?
if the floor is concrete then apply thin set ( this is not cement applied thinly) with a notched trowel. back butter the tile and drop in in. you can't install ceramic or stone directly to wood or plywood. even painted. you could use wonder board or hardie backer applied first, but I've had this stuff fail before. old skool way for wood get expanded steel mesh ( wire lath ) and put it on floor and nail or staple it to the floor. IT IS SHARP so wear gloves. you don't need to get it real neat and a gap uf a few inches is ok as long as that's not a grout line. then apply a good quality polymerized setting mortar, right hrough the mesh, such as versabond. you don't need additives just water.. you could also use flexbond if you want a little extra quality. when the floor sets up you have a very durable monolithic piece on the floor. I have been doing floors this way for years and I have never had a failure. I've even used it in applications where the deflection of the floor over it's span has exceeded the amount allowed. no failure and that's my ex, you gotta know that she would let me know. been 10 years if you don't get it right or skip the underlay or use mastic the floor will fail.. as noted by the grout coming out. the only cure for this is rip it out and start over.
More information is required. Are you placing tile on something? Thin set is for installing ceramic tile over a solid surface floor.
Use Hardibacker and seal the seams with tape and thinset. Use thinset to set the tile using 1/4 spacers. I have used and recommend that you use a tile sealer to seal the slate prior to grouting and to use epoxy grout. The grout is more difficult to install but requires no sealers which need to be redone at least once a year in a shower and is well worth the initial time and effort. Be sure to read and follow the directions on the grout bags to ensure a uniform color and good grout set. MT C