I have some apple and fig wood from trees that were pruned yesterday. The pieces range from sticks the diameter of your finger to about 3" in diameter.
How can I use these? Do they need to dry? For how long? Do I need to remove the bark?
Ideally, wood for smoking needs to be chipped, probably using a wood chipper though you could do small batches by hand using a chisel or bandsaw. Chips allows a greater surface area and gives a more consistent behaviour compared to large blocks of wood.
Whether you need to dry of not depends on several factors such as how old the wood is (I've never used apple or fig to smoke personally) and how much sap/sapwood it contains. While I have not tried with green wood, I suspect it would just take longer to catch as the fire you put it on will dry it naturally. Others on BBQ/smoking forums such as http://forum.bradleysmoker.com/index.php?topic=18832.0 say they have tried it and it works fine but obviously YMMV.
As for the bark - I would say for the smaller sticks where the bark is relatively thin then it's fine to leave on, but with larger branches I would remove it. In some types of tree the bark contains more oil than the rest of the wood (e.g. Birch), meaning you will get a blacker, sootier type of smoke that is generally undesirable for smoking food.
Apple and fig make great wood for smoking. Depending on your setup chipping is not necessary (I use whole or split chunks in my Big Green Egg), though if you are using a smoking box in an electric or gas grill, chips will be better. Do not soak your wood and it is not necessary to remove bark on woods from fruit trees, in my experience.
Any part of any plant (non poisonous) may be used for smoking if it produces nice smoke you like. No special treatment is necessary (soaking, chipping etc)
Just a handful of twigs or leaves will often be better than some tree trunk chipped up. New growth has more "flavour" than old wood or old bark
All you need is a small heat source and a BBQ with a lid. You can make a temporary lid from aluminium foil. Smoking without a lid requires a lot more smoke making material
Make the sticks into wood chips, and cut the bigger pieces into (roughly) fist-sized chunks. You will then need to season (thoroughly dry) your wood before using it for smoking. The easiest way to do this is to store the wood in an environment that will allow it to dry without molding, for a long period of time. It's a time-consuming process, but not one that requires a lot of active effort.