What is the best way to cook chicken for enchiladas?
Most recipes say to use a slow cooker, but some say boil. Why would one be better than the other?


It is better to slow simmer. As a very general rule, it is better to moist cook meat or poultry slowly. It makes for a more tender, more luscious bit of meat. Sometimes I'd rather not reinvent the wheel, so I'll just show you this from Bon Appetit to address the question of why.


  I plan on using boneless skinless chicken breast.


Certainly that is your prerogative! :) I would advise against it. In my opinion, boneless skinless thighs are best for this application, even though breasts shred more evenly and are just prettier than thighs. Again, I'm going to provide a link, this time for a recipe Add a Pinch . Easy!!


  I recognize there is no exact time for it to be done, so what are the signs of being done and ready to shred?


One of the reasons I love chicken thighs is that they are almost infinitely forgiving. You (for a few reasons, safety being perhaps the most important) should always cook chicken to an internal temperature of at least 165F (74C). In my opinion thighs are better much longer cooked than that, but that's the minimum for safety. When in any doubt, use a digital, instant read thermometer. That one and this one tied America's Test Kitchen ratings for best inexpensive models.


  Last question, how much water would I use in a slow cooker with the chicken? 


None :) Use a very small amount (2 TBS even) of something wet and flavorful! The recipe in the above section should be able to help with that. I use the "refrigerator velcro" (thanks Alton Brown for the great line) method. Open the refrigerator and look for something wet, Mexican-y and isn't spoiled. That'll work!

Good Luck.

I've left a lot of room for improvement in this answer and for more answers. I'm pretty sure the community has quite a bit to add.