When we are our picking fruit in Alameda, we notice that many backyard trees are in need of a good pruning. The ‘rule of thumb’ is that a bird should easily be able to fly through the tree. Citrus trees are, for the most part, quite resilient. You should never prune more than a third of any fruit tree, but in general you can prune citrus trees without worrying too much about doing it ‘perfectly’.
Prune smaller branches that are growing down or straight up, especially if they don’t have any fruit on them. Rub off small shoots with your thumb, which prevents new shoots in that area. Cut out any dead branches or twigs. If there are several branches in a bunch, pick the one that’s growing the direction you want it to, and prune away the others.
For a more specific guide to pruning citrus trees, please read this article by Jocelyn Prestwich.