Hi,
No, you aren't talking to yourself. Some of us just have to go do other things every once in a while and only get to check back here from time to time. 
The process is called several things: photo transfer, dye sublimation, heat transfer.
It involves converting a printer with special inks, to create a "decal" that is then applied to whatever surface you want it on. There are different types of "decals" for different types of surfaces.
I think the surface receiving the decal might also need some special preparation. This is particularly true of hard-surfaced items like mugs or tiles. I know these need a particular type of surface preparation, so you can't just use any mug or tile you happen to find. You have to buy ones specially prepared for this purpose.
You'll need one of the specific printer models s for which a conversion kit has been created. I believe my friend converted an Epson 13 inch printer such as a 1400 or 1280. As far as I know, it's a non-reversible modification to the printer, too, so, you'd never be able to use the printer for anything else afterward.
It is a heat transfer process, so a heat press is one of the more expensive items needed. The cost of that press depends upon the size needed for the work you'll be doing.
In the case of something like a coffee mug, the heat press would likely need to have some sort of adapter that matches the shape of the mug.
Also, perhaps there is a protective coating that can be applied over the photo, once it's on the mug, in the case of anything that's used like that and run through a dishwasher, etc. Must be, in fact, because I've got some photo mugs that are 10 or more years old and have seen a lot of use and cleaning and show no sign of fading.
If you do an Internet search with keywords like "photo, heat, transfer, dye, sublimation, heat press" I think you'll find a ton of info on this.
