Apply for a permit from your local zone ordinance office to cut any part of your native California oak tree. The native California oak is a protected species, and you will need a permit to prune yours, even if it's on your own property. Permit requirements, based according to the diameter and overall size of the tree, vary depending on the county.
Clean your pruning shears or saw off with a solution of 1 tablespoon bleach in 1 quart of water. This will sterilize them and prevent any disease from spreading.
Locate the branch bark ridge and collar of the branch or twig you wish to cut. This is the area where the branch attaches at about a 45-degree angle. The collar is the top edge of the ridge, in the V between the branch and the main trunk.
Cut the branch or twig with pruning shears or a bow saw as cleanly as possible at a 30-degree angle from the line you drew. Whether you use a bow saw or pruning shears will depend on the thickness of the branch you need to cut. A cut that is flush with the tree can lead to poor callus development. A proper cut made at a 30-degree angle to the trunk will leave a bit of a knob on the tree but will heal better and leave the tree less susceptible to decay.