To smoke meat, you want a relatively constant source of smoke, a low heat, time and water. A smoker is nice, but not necessary. Smoked meat stores well and tastes good re-heated, and a full grill's worth is no harder than one rib.
The water helps moderate the temprature--especially with a charcoal fire, as well as keeping the meat from drying out.
Low heat keeps the meat from being overdone before the smoke can soak in.
Take 3 medium sized steel cans and burn off all the labels and inner coatings. I currently use charcoal, and toss a couple of cleaned cans on the coals when I'm done cooking on the grill, to save for next time.
Fill all 3 cans half full of hickory chips. Fill one with water, one half full, and one with half an inch or so of water.
Light part of the grill, leaving part without flame. Put all three cans of chips on the hot side.
When you see smoke from one of the cans of hickory, put the meat or chicken on the side without flame and close the lid. Try to maintain the grill temperature around 250 or so.
Periodically check the hickory cans. Eventually one of the cans will finish smoking--dump the coals (into the fire if charcoal, into water otherwise) and half-fill with hickory, fill with water and put back on the fire. Keep repeating this. Adjust the amount of water so that one can is starting to smoke as the other one finishes. If a can boils dry before the other cans are done, add water.
Cooking at 250, the meat will generally be fully smoked about the same time it is done. Pork chops take an hour or so, thicker ribs or chicken 3 or so. The meat will be pink, but either even pink, or darker from the outside. This isn't the same pink as underdone.
Don't put BBQ sauce on until the meat is done. I've quit putting sauce on the meat at all--instead I heat up a small bowl of sauce and dip the meat in as I eat. I like Montgomery Inn sauce--tomato based, not too sweet, the right amount of bite.
You can also use foil packs of wet hickory chips instead of cans. Make a foil envelope about 4x4, put the hickory in and seal, poke a couple of holes in the top. When the smoke slows, put another pack on. If you are using foil packs, you probably want a pan of water boiling on the grill as well.
A meat thermometer left in the meat will get coated with smoke and hard to read.