Before anything else, a strong caution: I am not some guy who has been laying tile for 20 years. In fact, this is my first go at it. Although I'm describing my thought process and various decisions, some of those things will be based on my assessment of my own abilities and energy. If you are a guy or gal who has been laying tile for 20 years, you might even be laughing at some of my exposed ignorance. In any case, if you are a novice tiler like me, take this info truly for what it's worth. There are both aesthetic and functional components, and I might be wrong on particular points of either. YMMV, etc.

Some time ago, we suffered the dreaded water-from-the-ceiling telling us that there was some kind of leakage problem in our main upstairs bathroom. We had a plumber in, and he replaced the drain assembly from the tub which, he said, pretty much came off in his hand when he was inspecting it. Alas, it turned out to be that bane of diagnosticians everywhere: two problems instead of one. The drain needed fixing and got fixed, but the water continued to come. 

After a considerable amount of head-scratching, I figured out that the water was coming through the walls of the tub surround. It's a typical combined tub and shower arrangement, and water hitting the tile walls was seeping through. I covered things up with a combination of a plastic shower curtain and some duct tape. A work of art, I am sure, but it stopped the leakage until I could do a proper fix. When I finally got some time on my hands, I set aside an entire weekend to re-do the grout around those tiles. That turned out to take considerably less than an hour. After removing the old grout from around a couple of tiles, in the trouble area the tiles fell off the wall. The backing material was also looking kind of groggy. I knew then that things would probably need to be stripped down to the framing and built back up. I re-rigged the plastic and duct tape to give myself time to think about next steps.

The recessed cut-out on the right was for the (removed) soap dish.

I already knew that re-tiling would be a big job, and I hadn't decided if I could do it myself or would need to hire someone. A little bit of investigation of outsourcing costs soon convinced me to make an earnest study of whether I could do it myself. A turn of circumstances in the household, details of which are not relevant, forced a 2-3 month delay before I could start, so plenty of time to evaluate my options. As you can easily tell, I did decide to do it myself, and this is the story of that process.

And remember, for any big job, it pays to get a second opinion from a trained expert: