I am actually making some pulled pork right now so this is fresh in my mind. Firstly, to make pulled pork or beef you will need a crockpot or electric stove. Do not try this with a gas stove. I find that pork loin has the best quality/cost ratio for this, but most cuts of meat can be prepared like this.
Basic pulled pork is made by just barely covering the meat with water, spicing it, and then cooking it. The key to getting that soft, easy to pull apart texture is to slow cook the meat. This is done automatically in a crockpot. On a stove you want to heat the pot on the lowest power level. This depends on your stove of course, if it is very weak you might want it to be at 2 or 3. On the other hand, if the pot boils on the lowest setting, you are screwed.
You want the water to get hot, but not to boil. A light simmer should do. If you are worried about infection you can just boil it for a few minutes at the end of the cooking cycle. Once you get the water up to temperature, cover it and leave it for a couple of hours. The minimum depends on how big a piece of meat you are using and its surface area. Four hours should do it for most cuts, and there really isn't an upper limit.
For the spicing there are several ways to go. The basic mix that I use I call the Italian Mix, is just a good dose of ground black pepper, with italian herb mix. The italian herb mix can be bought pre-mixed, or you can throw it together yourself (Which I recommend). I use 3 parts Basil, 5 parts Oregano, and 1 part Rosemary.
You can also make a gulash by tossing in some carrots (peeled baby carrots are the easiest) along with crushed tomatoes and some onions. Potatoes are optional. The spicing here is a little trickier because it uses paprika, which is one fickle SOB. Use a good amount of garlic powder, cumin, corriander, cilantro, black pepper, and basil. Then add a touch of paprika or chili powder. This gives it its trademark taste and color.
The other spice combination I can think of off the top of my head is: Caraway, taragon, touch of sage, and a little bit of ginger. It can a little tough to get the mix just right, but is an interesting change.
One of the advantages of slow cooking is that you can adjust the spicing as you cook it. Just take a little taste of the water/sauce and adjust as needed. You can also make it in the oven, but I have never tried this. I think SteelyD does that on his thread, which you should read. Because it is awesome.