How should chicken breasts for a chicken salad be cooked?

It really depends on the texture you are looking for in your finished product. If you want a chunky chicken salad then bake your chicken breasts seasoned or not, I season mine, and then cube them. If you want something a little more exciting pan grill the breasts to the point of a little char and then dice. If you want your chicken to be flavorless and get all of your flavor from the mix you are tossing your chicken into, boil it or put it in a slow cooker if you are cooking up a big batch.

It all really comes down to how you like to eat your chicken salad, and more importantly how pretty you want it to look in your serving method, because a cajun blackened chicken salad sandwich can look down right homely. I say try them all until you fall in love with one temporarily and when that has lost its passion try a different version.

Also as a side note if I am preparing it for me and not for someone else, so it doesn't have to be all white and pretty, I use thighs instead of breasts since they are more forgiving and generally cheaper. If I am not just breaking down a whole chicken and using the leftovers.

I prefer simmering a whole bird to get shredded chicken, like Satanicpuppy. That should take an hour or two to accomplish.

For a chicken salad that has cubed pieces, I would saute or grill a whole breast, then cut it up afterwards. You can bake it, but it takes longer than the former methods. You can also slice it up beforehand and saute it- that is a much faster option than any other. Just make sure you season the breasts; they will be virtually flavorless otherwise, and make your salad dull. I'd use garlic powder, salt, freshly-ground pepper, and saute it in butter.

I usually do a whole small chicken in a pot with the traditional herbs, onions, celery, etc. Cook it slow until it falls off the bone, strain it, and let it cool before picking the meat off.

That being said, I've gotten perfectly decent results using store bought rotisserie chickens.

Roasting and pan-frying provide the most intense chicken flavor and make the tastiest chicken salad. Both have the added advantage of some browned scrapings to add to the savory flavor of the salad.

There are many ways to cook chicken AKA: apply heat to chicken to bring it up to a safe 160 degrees. Most old school recipes have you boiling the chicken. This is wrong on many levels with the biggest reason you are dumping most of the flavor down the drain when they are done. I wash then bake my skin-on rib-attached chicken breasts at 350 until they reach 159 degrees. I then take them out and let them cool where carry over heat will take above 160 degrees. Let rest covered and unrefrigerated (OK for up to 2 hours) with plastic wrap for 90 min. Throw away the bone and skin and chop. YUM.