Of all Filipino food chicken adobo is by far the most well known (it's the only one that has YouTube videos about it in Engilsh) but like all Filipino food recipies are scarce becasue, as I have learned from personal experience, Filipinos don't use recipies and therefore don't really understand them. While I was on my mission there an American freind of mine asked a chef guy we knew for a recipie so he wrote something along the lines of, "6 chicken, 2 soy sauce 2 vinegar, 4 onion, 6 garlic . . ." and no actual instructions. We had no idea how to interpret 6 chicken, was it kilos of chicken, pieces of chicken, whole chickens? A few months later I asked one of my companions how to make it, one thing he said it needed was spices, so I asked him what spices and he resopnded with something like, "you know onion garlic and ginger" at that point I gave up learning how to cook Filipino food while I was in the Philippines. But with some trial and error I finally figured it out.
First you want to deal with your chicken, If you want to be as authentic as possible you sould buy a whole chicken and use your heaviest knife to chop it uncerimoniously into roughly bite size pieces, choping the bones and everything. If you don't want to do that at least make sure you get some chicken with some fat on it. There is no reason to be afraid of fat, and if you are then you should never leave America.
Optionally you can merinade your chicken, I don't think I ever actually saw a Filipino do it (at least in person) but it still wouldn't hurt and you don't have to do it for long. You want about an equal mix of soy sauce and vinegar, enough to cover your chicken. You'll also want to add aproxomatley an eight of a cup of brown sugar or honey, some bay leaves, and at least a dozen or more whole peppercorns.
While your stuff is marinading you can chop your vegetables. Dice your onion and garlic into the smallest peices you have the paitence for, I can't explain why it is better when they are absolutely microscopic trust me it just is, the ginger however does not have to be chopped that small.
Once your stuff is chopped oil your pan and throw in all the stuff you just chopped along with your chicken, save the marinade because because as soon as your chicken is mostly dooked you'll dump all of that into the pan as well (waiting is probably uneccecary but I'd rather not risk food poisining). Continue cooking until most of the marinade has boiled off, then you're done serve it on some white rice and enjoy.
* This could also be done with pork but it is hard to find pork with enough fat for this to taste good in America (you want cubes that are at least 40% fat)