Apply grout with a rubber float working diagonally across the tile.
How to install tile backsplash on uneven wall.
Spread the mortar with the flat edge of the trowel then groove.
A professional installer would use a pair of scribes to transfer the contour of the wall onto the top edge of the counter top then use a circular saw or a belt sander to take off the area of the backsplash where your wall is bowed out.
Back buttering back buttering is a trick used for tiles of uneven thickness like ungauged slate or handmade tiles extremely large tiles or for tiles being installed on an uneven surface.
Mark the wall at the top of the tile.
Follow the lines you made when the tiles were dry fit to the wall.
1 4 inch is not too much to take off provided your cabinets do not measure anymore than 24 from wall to front of face frame.
This ensures the tile adhesive secures to the surface.
Then use a level to extend the line along the work area.
While you volunteered to set tiles is repairing rebuilding the wall something you even want to deal with.
That is what i would do so it could be painted i would not even try to tile over the patch job you described.
Slightly rock the sheet up and down perpendicular to the trowel lines to collapse the ridges and help the tile settle into place.
Use tile spacers if necessary to keep the tile lines straight in the layout.
Shop for tile tools.
Shop for tile.
First use a level to find the lowest point of the countertop.
Spread thinset mortar on the bottom center of the wall.
Learn how to install a tile backsplash.
If existing tiles are beyond repair remove the tile and install a piece of wallboard in its place.
Mark the two sides of the wall using the painter s tape where the backsplash should.
Place the mosaic sheets along the wall.
Like bill pointed out you are unlikely to end up with a flat enough surface to get a good tile job unless you use very small tiles.
Hold the float at a 45 degree angle as you work the grout into the seams.
Shop for grout and mortar.
Wash the wall with tsp tri sodium phosphate or an ammonia based cleaner to remove any grease or oil.
Backsplash installation in 15 steps.
Clean the wall thoroughly with the cleaner to remove any grease or other debris.
Ready to get started.
Do not grout the bottom seam where the tile meets the countertop you ll want to use caulk in that seam.
Hold a tile at this spot accounting for a 1 8 inch expansion gap.
Add tile spacers for help keeping the tile pieces lined up.