Are we talking rough slate or slate tiles? Rough slate come in irregular shapes and ranged in thickness from 1/8 to 3/4 inch thick.
Slate tile has been cut into squared pieces, planed and sanded down on one side to a consistent thickness (3/8 to 1/2 inch thick depending on the slate and the use) Tiles have a rough side (obviously scratched with straight lines) and the pretty side which is rough as well but in a natural way.
If it is the first, well that will require a thick coat of mud on the wall, after you wire and scratch coat.
If it is tile:
If it is going directly on to brick then you need to clean the brick with ammonia to remove as much oil and soot as possible, then use a product like Masonry (wall tile) Adhesive (comes in assorted colors BTW). That comes in a tube and is sort of like liquid nails. It also comes in tubs and is applied with toothed adhesive spreading trowel. You will need spacers and start from the bottom and work your way up using your plastic spacers
http://www.tiletool.com/one/tile_spacers.html They are sold at home stores, but just to give you and idea of what I am talking about.
Then you will need to apply grout.
On Dry wall I would rough up the surface of the paint (sanding) - if there is wall paper remove it. Clean (soapy water) and rinse and go on from there.
Cutting Slate can be fun. Slate is a soft stone, very soft. I have successfully sawn slate roof tiles in half using a hand saw - yes I ruined the saw, after 5 cuts - but it was a small job and I did not want to rent one of these:http://www.tile-saw.com/mk100.html You can rent one from home Stores and some hardware stores.
I have successfully drilled a hole in slate using a hand drill - the one with the handle like the old fashioned egg beaters - human powered. I have drilled many holes in slate for roof using regular masonry bits. Slate is a soft and tender material it readily cracks if you put too much pressure on it If you try to cut it to fast it will chip.
If you have something along the lines of 5-8 tiles to cut, mark them for cutting and take them to home Depot or Lowe's, they may cut them for you there free of charge - if the guy is nice. If you are doing more than that, rent a wet saw.
I will assume you will have a nice grout to finish off with, grout comes in many colors, is really fast drying and real easy to smear into the the cracks between regular ceramic tile. When it comes to slate you will want to refrain from smearing it all over. Slate is soft and porous, thus your grout will stick to it and ruin the surface.
For a thin line, I would use something like tube caulk a latex based one (They come in so many colors now days!), nipping the tip of the tube for the smallest of holes, that and a steady slow hand to fill the lines, following up with a damp finger to press it in.
For 1/8 to 1/4" seams I would "pipe" my grout material into the cracks. Like decorating a cake.
I would seal with a Low Sheen Sealant Finish product there is a one step product on the market by Aqua Mix which I have used before. The slate looks kind of dull, just enough finish to make the interesting lines and shades of coloring pop.
While you are at Home De-Pot or Lowe's go to the tile area and ask the tile person for the best products, there are so many out there which make the job easier for the DIY person.
David