I have a fig tree that is 5-10 years old. Currently I just remove the dead branches. What is the proper technique for fig pruning?
Fig trees unlike a lot of other trees out there do not mind being pruned a LOT. What I mean by that is you should not be afraid to prune this type of tree. If they have a really good root system they can withstand a harsh pruning (harsh in a good way :)). Within the first year, provided that your fig tree has established itself is a prime time to prune. You will want to select a few branches to keep as your fruit that can be picked for the time being, the rest can be pruned away.
The best time to prune the tree is in the winter season or late fall when the tree is not growing.
You have the right idea, get rid of the dead branches first as those do not serve any purpose at all, they may actually hinder the tree if they have any type of disease on the wood. If you see any suckers remove those from the tree as well.
After you've gotten rid of the dead branches and the suckers you will want to remove any branches that are very close to the main branch, these branches do not yield fruit or yield very little.
For larger fruit and better growth make sure you prune the rest of the branches about 1/4. This is especially important for the upcoming season and will help yield more fruit for you. It's probably one of the most simpliest trees to prune, because it can actually take a lot of pruning without any affects (as opposed to prunining rose bushes / trees).