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.

As you're new to cooking, I'd actually advise you use the boneless skinless breasts that you mentioned, just because they're easier to deal with ... even if they don't have as much flavor.

Although a slow cooker will work (I like canned chipotles for liquid, but I like heat), if you don't have one, or don't have the time to wait for it, here's my technique that's relatively fool-proof:

1. Fill a pot (large enough to hold the meat with plenty of room to spare) about 1/3 to 1/2 full of water, and set it over high heat.
2. Add whatever sad-looking vegetables you might have (onions, garlic, bell peppers, carrots, celery, maybe some peppercorns, etc.), but not so full that you won't have room for the chicken plus some extra space.
3. Wait for the water to come to a boil.
4. Add the chicken, and put a lid on the pot
5. Wait for the water to come back to a boil.
6. Set the burner to low (or medium-low, if it's a really large pot, or you know your stove to be under powered)
7. After ~30-45 minutes, check the texture of the chicken. (using tongs, grab one, and if it falls apart, or if you can tear it with a fork, you're done ... note that if the breasts are of different sizes, they might not all be done at the same time; exceptionally large breasts might take an hour).
8. If not done, check again in 5-10 minutes. Repeat 'til it's done.
9. Pull out the chicken and shread it.
10. Leave the broth to cook while you're dealing with everything else.
11. Strain the broth, and save it in the fridge for some other use.

You start off boiling, to help kill any surface bacteria on the chicken. We then let the water cool down and cook it slower to both get the fall-apart texture and to give a longer window of done-ness. It's really difficult to over-cook it this way.