At the core of braising is cooking with a low heat for an extended period of time (usually 250-300 degrees for 3-4 hours). It is the same principle actually as slow barbecuing. You want a slightly moist heat. This technique has been used for hundreds of years to make lower quality cuts more palatable. But we're not doing this just to use up that freezer burned chunk of chuck in your freezer. No way, braising can produce flavors and textures that you only hope you could taste let alone reproduce. And guess what, you can. Even better? It's actually quite easy.
Imagine a pot roast that you can cut with a fork AND slice with a knife (and have it not fall apart) all the while being perfectly juicy and tender. Or a weird cut like oxtail or shanks that is impossible to cook any other way and comes out so rich that you'll get all poetic at the table.
So here's the rules, just don't violate them and everything will come out peachy.
1) Slow and Low - Just have to reiterate it, it's kinda integral.
2) Sautee your cut and veggies - this produces "Fond" or the tasty charred bits at the bottom of the pan
3) Deglaze (add liquid) - bring to a boil to release the fond. Reduce to half (this is your brasing liquid)
4) Cover and Cook (yup you guessed it) Slow 'n' Low.
The end result can be devoured right off the bone, or pulled off and shredded for sandwiches. Give it a try, you'll be so happy you did.