First I made my base by screwing 3/8 inch hardiboard to 3/4 inch playwood
I wasn't sure how to attach this, but the hardiboard had a grid on it that looked like it wanted me to put screws there, so I did. I had planned on attaching like I would underlayment, and the grid layout was about the same, so this seemed to work out well. I then attached my tile using thinset, I didn't leave any spaces between the tile, so I didn't need to grout anything. I talked Julie into helping me lug the heavy thing up stairs to the laundry room and attached it to the cabinets. I trimmed out the counter top with 1x2" oak trim that I stained to match the cabinets.
This came out looking pretty nice, but the walls have some wiggle in them, so the edges weren't really tight with the walls. They were close, but there was up to about a 1/8" gap in the worst spot. Not a deal breaker, but large enough to lose things in and didn't look all that nice. I had thought I was going to make a backsplash out of 6" granite tile (just the normal tile cut in half), but 6" looked pretty gigantic, so I decided not to do that afterall. Instead, I got another piece of oak trim and stained and trimmed. I just put a chamger on the edge of the trim to match the edging, made a little corner block and nailed to the wall.
I made little mitered returns at the edges of trim to hide the endgrain, caulked the edges with clear silicone, patted myself on the back and declared it Miller Time (well, Ithaca Beer Company Time, if I'm being honest!).