Gas grill: soaked wood chips vs. dry wood chips

Don't bother soaking them. Dried hardwood doesn't readily soak up water, so for this to work you'll have to either soak for a rather long time or start with green wood... but if you're using green wood then you don't need to soak it.

For good, consistent smoke, you want to control heat and airflow: as hobodave notes, you can control heat by simply moving the chips away from the coals. If the design of your BBQ allows, you can do as he suggests (horizontal separation); otherwise, try placing the chips in a pan above the coals.

For airflow, you can adjust the vents on your BBQ - if you're getting flair-ups with the lid on, chances are you're letting too much air through. You can also limit airflow to the chips themselves by wrapping them in a packet fashioned from sturdy aluminum foil with holes punched in it (but you'll still want to separate them from the coals, or you'll just burn through the foil and be back where you started).

You can use a gas grill for smoking and indirect cooking. Run the burner on one side of the grill, and place the food on the other. Wrap wood chips in foil, poke a few holes in it, and place the foil pack over the active burner. You can soak the chips if you like. I've never seen much point in that, myself. The water evaporates rather quickly, and you're back with dry chips. Better to limit the oxygen supply to the wood so it will smolder, and place the smoke pack somewhere so that it does not have too much heat applied to it.

It absolutely does matter what kind of wood you use. Avoid soft and sap-laden woods like pine. Stick with hardwoods or fruit woods. Hickory is often paired with pork. Apple and cherry are used ubiquitously. Oak is strong, but imparts an interesting flavor. Mesquite can be too powerful for some people -- I personally use it for grilling, but never for smoking.

Finally, be aware that you are going to have some limitations with your gas grill. It neither holds nor convects heat in the same manner that purpose-built smokers and some charcoal grills do. You are more likely to have hot and cold spots on your grill, so you will need to examine what you are cooking each hour and adjust accordingly if necessary. You will also not get nearly as much smoke to your food, so you will also have to adjust how much wood you use accordingly (though many people make the mistake of too much smoke in their barbecue, so a gas grill's limitation in this regard can be a benefit).