Hi there, welcome to the site
Your question is a bit broad, so you might have some difficulty getting a lot of responses to this particular post (it's not that people aren't friendly/helpful here, but my goodness there's so much info that they may not know exactly where to start). If you're new to the site in general, you might want to start here:
What is cg?!
TON of useful information for new curlies!! =)
Understand that not everyone on this site is strictly CG (some no poo, some love a sulfate cleanser on the daily; some avoid petroleum, some
for grease; some scoff at the very idea of silicones, some won't detangle without 'em) . You will have to play around with a few techniques and products to find the right combination to suite your particular needs.
As for your dull hair/breakage:
1. Straight hair tends to reflect light (thus appearing glossy/shiny), but kinkier/curlier hair tends to refract light (which can give 4a/b hair a dull appearance). This doesn't necessarily mean that ALL 4a/b hair is damaged or dry, it's just the physical properties of our hair. If you want to boost the shine of your hair, you could try incorporating oils into your regimen--or buy a moisturizer with oil in it (this shouldn't be hard to do since most moisturizers have some sort of oil in them).
2. You will want to cut off the damaged hair (you can do that gradually or all in one chop). If you allow the hair to just break off, it will break off and form split ends which will just lead to more breakage in the long run. Try to keep the heat styling to a minimum for now. Experiment with defining your curls, twists, coils, braidouts, pony puffs, or a 'fro--basically, just try styles which do not require heat. Lastly, try doing a weekly deep conditioning treatment. If your hair feels brittle/dry, it could be because your hair lacks moisture.
I tried to make this a short post, but I get a little ranty sometimes. Hope this isn't too overwhelming.