You can put it onto the drywall. You want it smooth and to not have a glaze, so you may have to sand it. If its been painted with a topcoat, you may want to paint it again with a primer.
Use mortor that is specifically designed for glass tiles, not ceramic tiles.
Everything Matthew said is accurate, good answer if you're mounting very close to the ceiling. A ledger is a good way to keep the uppers aligned and support the cabinet weight while installing.
There are several other techniques you should know however.
1) Screws holding the weight should be through a framing member or stile, not through a thin backer panel, they should go into a stud or a horizontal nailer installed between studs for this specific purpose. you may have to remove a strip of sheetrock to install a nailer. Do not screw into just sheetrock, even with anchors or your cabinets will be on the floor before you know it. Don't use drywall screws, get cabinet screws that have a built on washer.
2) Adjacent cabinets need to be clamped together and fastened together through the side stiles with counter sunk screws. This locks them together and assures the meeting stiles are flush and stay flush.
3) Always start in a corner if you have cabinets going down two walls. the corner cabinet is your anchor.
4) Carefully check the level of the floor and use embossing material to fill and sags or dips.
5) Dry fit the lowers, before attaching to the wall, shim the low ones, clamp the adjacent stiles together as you did with the uppers. Screw them to the wall, checking level in both directions (length and perpendicular to wall), then screw the stiles together as above.
6) measure precisely the openings required by your appliances. Give yourself no more than 1/4" over the actual appliance dimension. 1/8" is better. 1/16" on either side.
7) Install the lower kick plate last to cover and shims and gaps.
There are a lot of other tricks of the trade, but go slow, pre-plan and have a little extra man power to handle the cabinets.
Google up "This Old House" and watch some of the many videos on this topic.
Best Answer
Why would you want to tile first, then lay cabinets on top of the tile? This ensures two things:
The person in the future who wants merely to replace the tile while not touching the cabinets will be cursing your soul to eternity. Remember, this might be you cursing yourself, if for some reason it turns out you need (or merely really want) to replace the tile.
That you will spend more money on tile than you need to spend. Tile is expensive, so why throw money away underneath a large block of cabinets?
Place the cabinets first, then butt the tile against them. Yes, you will be cutting some tiles to fit. Tile cutters are not difficult to use.