How do I cook chicken thighs on the stove?

This way: http://cooking.nytimes.com/recipes/1016135-rishia-zimmerns-chicken-with-shallots

Sometimes I grill them on a grill pan with an olive oil marinade. Then we use them for a variety of dishes.

Once the skin and bones are off the chicken, there is very little fat left. I would not remove it. Most chicken has very little flavor, and the fat helps with that problem. Vegetables are usually added to the pan after the meat has been browned. I usually remove the meat, brown the vegetables, then add the meat back to the pan before adding whatever liquid you are using in the dish.
What are you making that you want to cut them into small pieces? Or are you just interested in cooking it as rapidly as possible?

It would help to know your recipe plans in order to give you the best suggestions.

Here are a few recipes to check out that all cook on the stovetop: https://food52.com/recipes/35813-canal-house-s-chicken-thighs-with-lemon, https://food52.com/recipes/20892-braised-chicken-thighs-with-tomato-and-garlic, https://food52.com/recipes/18223-chicken-cacciatore, https://food52.com/recipes/34205-chicken-thighs-with-tomato-orzo-olives-and-feta