With all due humility, I must confess that I am (locally) famous for my ribs.
Here's the trick for superb bbq-d ribs, either pork or beef...
<looks left - then right - coast is clear - nobody's reading>
Cut ribs up (singles for beef, "twosies" for pork) and place them in a large, lidded pot of cold water. (I say "large" because I always cook at least two racks at a time and usually four or five.) Bring to boil.
IMMEDIATELY upon coming to a boil, turn the heat down and skim off the surface scum that's accumulated. When the water has settled into a slow simmer, put the lid back on, but ajar, lest it come to a boil again. You should just see occasional, faint little bubbles. (If the ribs boil for any longer than 5-8 minutes, you might as well eat your shoes.)
Simmer the ribs for at least 45 minutes. An hour is about perfect. (Simmer too long though, and they start falling off the bone. You don't want that to happen 'til they're on a plate.)
Drain and lay ribs out on a foil-lined baking sheet. (At this point, the ribs are actually cooked. Now our job is to add flavour.) I like to season them with garlic pepper and Montreal steak spice. If the latter isn't available where you are, use your favourite mixed herb spice (as long as it has lots of garlic).
I like to spray the ribs with a light coating of Pam-type cooking oil spray before slathering on copious amounts of bbq sauce. (During this process, the bbq is pre-heating.)
With the bbq heated and then turned to low, put the sauce-slathered, meaty sides of the ribs on the (Pam-sprayed) grill. While they're (re)heating, brush sauce on the undersides of the ribs. Close lid (unless your bbq burns pretty hot).
After 3-6 minutes of cooking (don't let them scorch too much) turn ribs over and re-apply more sauce. Close lid again. After a couple of minutes, I turn the propane off and just let them stand in the bbq for another couple-few minutes.
Serve, and try to appear modest when the accolades roll in.
Sauces: For beef ribs, I like the Bulls-Eye sauces, made by Kraft, especially the Bold Original. These are strong-ish, pungent sauces that compliment beef nicely.
For pork, I usually go with a sweeter sauce. Many of the store brands of chicken n' rib or honey & garlic are acceptable (as long as they're thick - don't like a runny sauce.)
There's one particular sauce available in Canada that I like with either beef or pork. It's the President's Choice Smokin' Stampede Beer & Chipotle sauce available at the Loblaws' group of stores.