How to clean a Brick Hearth

Personally, I like the look of naturally discolored and charred brick. It looks better than trying to scrub off the face of the brick to a point they don't match the rest of the brick surround.

Ok DannyBoyBlue I hope these are some solutions for you.
You say that your fireplace is used fairly consistently for about 5 months out of the year so lets assume what we’re looking at is quite a bit of smoke and soot buildup to deal with. Before starting any of these make sure you put down something to protect your floors and surrounding area as well as a mask to protect yourself from any dust and ash and a good set of gloves. I’ll try to keep these as kid safe as possible.

One solution consist of an alkali base detergent and water mixed and sprayed on. Spray it generously, let it soak in, then use a scrub brush to remove. You can add an abrasive element to this mixture but you may have to alter your application method for this.

Another solution is white vinegar and water. Dunk your brush into the solution then have at it. This one is a bit tamed so be prepared to take multiple passes at it.

Outside of that there is of course the general cleaning like removing ash, cleaning your fireplace screen, etc. Any cleaning you do can, and might discolor your brick work so try these on inconspicuous areas first to see what your result would be. Also sometimes cleaning can leave a “haze” to the brick work depending on the color. You can combat that with an application of 50/50 boiled linseed oil and mineral spirits. I’ve heard arguments for both using the linseed oil “raw” and some for “boiled” so that I leave up to you to . Hope something in this is of use to you. Exercise caution and always test a given solution first are the rules of the day. Search the web and you'll find plenty of discussion on the linseed oil.
Cheers,
ChrisFixit

Thanks for the speeding reply. I appreciate the "good" ideas.
I'll start with the vinegar solution. If that doesn't do it, then I'll try to figure out exactly what is an alkaline based detergent. When you say detergent, laundry or dish soap comes to mind.
Unfortunately my chimney sweeper was reluctant to share advice on the exterior elements of the fireplace.
Occasionally the glass door to the insert gets a carbon build-up, depending on the type and condition of the wood I burn. I've used non-fuming oven cleaner on the glass with great success, ignoring recommendations from the Easy Off people. But hey, it's quick, easy and efficient. The dirty brick, which is a flat surface below the door is the only concern and you've been more than helpful.
Again, thanks for the sound advice.
Best regards,
DannyBoyBlue

PS. We love Atlanta. Got family down there, too.

a little off topic but mixing water with ashes into a slightly pasty substance is the best fireplace,woodstove glass cleaner i ever used.use newspaper to apply and remove then throw paper in fireplace