What You Will Need
First things first, you need to find yourself a good sized pan. Note that it doesn't really matter what type of pan you use exactly, so long as your flour tortilla will fit nicely inside it. (I find that a frying pan suits my needs perfectly for this.)
Flour Tortillas - (your prefered size)
Chicken Breast - it's up to you on how much you will need, but in my experience breast tenders (chicken breast cut up and sold pre-packaged in strips) runs me around $4.00 for a pound which will give you around 7 or 8 quesadillas, possibly more depending on how much chicken you like to fill it out with.
Shredded Cheese - I buy the nacho taco blend shredded cheese which is my local supermarkets store brand, and is quite good for our purposes.
Optional - Veggies such as chopped tomatos, green or red peppers etc. salt, pepper, or any number of seasonings for the chicken which you may decide upon. (personally, i use Montreal chicken seasoning. A bit unorthodox for this type of food perhaps, but i love it)
1) Take your chicken breast strip(s), one should be fine, two if you like it more on the meaty side and start to cut them into bite sized pieces. The pinkish parts are what you want - this is the meat. You will want to trim the undesirable part, which is the stuff thats white, and can be pretty tough to cut because of it's elasticity.
2) Now that your chicken is clean and cut, you will need to season it with the spices/herbs of your choosing. (to go the really simple route, just throw some salt and pepper on all sides of the chicken)
3) Use your cooking spray and lay down a thin layer on what you'll be cooking your chicken on in the oven.
Execution! (NO! not that kind. Put down that knife!)
1) Pre-heat your oven to 350 degrees fairenheit, and after it pre-heats, cook for 7-10 minutes depending on the size of your chicken. You will need to watch it to make sure it doesn't become overdone. (A good way to check the chicken is to cut one or two pieces down the middle and to check if they are completley white with NO PINK, which is a sign of undercooking and could potentially make you sick)
2) While the chicken is in the oven, pour a circle of vegetable oil (about the size of the bottom of a regular drinking glass) in the center of the frying pan and spread it over your cooking area by placing your tortilla on top, and moving it in a circular motion with a spatula. Wait a few minutes for the tortilla to crisp, and when it is as done as you like, flip it over and do the same with the other side (minus the oil part, since you already have some on the pan).
3) With your chicken now cooked and waiting nearby, while you are wating for the second side of the tortilla to finish, place the shredded cheese all over what will be the inside of you quesadilla. When the cheese has melted, you can shut off the flame, and place your chicken and other goodies (veggies, or whatever else you want, I'm not the boss of you) on top of that melty goodness, fold it in half, and call it a day.
4) This step should really be implied, but for the slower amongst us...IT'S TIME TO EAT, MAN!