Ok, I am a big believer in doing this, it will turn an unsightly dark fireplace into the focal point and lighten a dark room substantially.
However, remember, a painted fireplace cannot be reversed. So, one whack of paint and your committed. Do you plan to stay there forever? What do you think the next homeowners will think of the painted brick? Are you sure??
1 remove all the stuff from the area and wipe clean with vinegar and water solution.
2 get some paintable caulking and caulk or fill in cracks, holes, divots and the like.
3 get a gallon of Kilz primer and begin the job of about three coats of primer. Of course let a good 3 hours of drying between coats. I would use all latex for primer and final coat.
4 get two gallons of quality latex interior paint in a semi gloss or emanel. I stress a quality paint, not one from a home center.
5 Paint on another two or three coats. this should do it.
I do this quite often for customers and I always use 5 to 6 coats of paint. I have heard others say that it can be done in one coat of primer and two coats of finish. I have tried this and the surface and coatings are not of quality I want to achieve.