When I smoke most items I use what I call an Indirect smoke. It comes from a side box on the non gas side of my grill. The smoke box is mounted over the vent hole on the side of the grill.
I use hardwoods and keep the fire very low. Different hardwoods for different meats. I'll use fruit woods for mostly Pork, Oak, Hickory or Mesquite for Beef and maybe a combination of both for chicken depending on were I am going with the chicken. I,m not a big fish fan unless it's fresh caught and I'm eating it right away.
If I am using the gas side of the grill and want to smoke something I do soak my wood chips, place them in a foil pack that has holes poked into the top to allow the smoke to escape and place the foil pack down by the gas burners. I have a little rack I made up to set the foil pack on so it's under the grill rack just above the flames. I try to keep the heat down to about 200*. Depending on the smoking time I will replace the foil pack and chips several times through out the day. Drawing the smoke just right over the meat or even vegetables is important too and controling the smoke inside with the opening and closing of the top vent. This also controls the heat.
I have seen some variations of smoking where green woods have been used but these are more of a pit roasting type or method. I have seen the use of green bamboo and other wet land type woods used, also leaves and sea weed. I think these techniques are for more of a steaming method though, not really what I call smoking, drawing the flavors from the woods or leaves to infuse into the meats.