I toss boneless skinless chicken pieces in a pot with enough water to cover, and simmer until it pulls apart easily and is no longer pink in the middle (usually not more than 20-30 minutes depending on size of pieces). Try not to overcook it, or it will lose too much flavor - I cut what I buy in half, and start checking at about 20 minutes.
Then I cut it up and use it in dishes that the chicken flavor will largely be overpowered by the other ingredients anyway - casseroles, soups, chicken salad (the kind with mayo that you would spread on crackers or bread). I do not do it this way if I am serving the chicken alone, or in strips on a green salad, etc - for that, we mostly use the grill, and often just marinate in bottled or homemade Italian dressing.
This also does NOT make a stongly flavored stock, but if you add some onion and garlic and whatever other spice you like (either with the chicken or afterwards - with the chicken will give it a bit more flavor also) then it's perfect as a start for soup (the veggies you put in that will add to the flavor, or you can add some purchased broth if you prefer, but if you use this, you won't have to buy as much) OR for cooking rice or noodles for a side dish - stuff that you would normally just use water for - this give it a little bit of chicken flavor. I freeze it and mostly use it to make side dishes for a chicken entree, and my daughter loves to cook plain wavy Chinese noodles in it for lunch ( this = homemade ramen without the msg in the purchased flavor packs! We buy them at Whole Foods but your local market may have them too) - she just seasons it the way she likes, usually onion/garlic powder/salt and maybe a little poultry seasoning.
Good luck and holler if you have any more questions. I do a lot of very "basic" cooking but my family is always happily well-fed. :-)