If branches are partially dead -- needles yellow but the branch still flexible and full of sap -- wait until the branch fully dies. If this branch poses a hazard, immediate removal is warranted. If you choose to undertake all pruning tasks at one time of year, late winter to midsummer is ideal.
At the base of the pine branch is a swollen area immediately around its connection to the trunk: the collar. Do not cut into this collar when removing the dead branch. Leaving the collar protects the trunk and helps prevent rot or other pathogens from gaining direct entry into the vascular tissues.
Susan C. French and Bonnie Lee Appleton of Virginia Cooperative Extension recommend removing entire branches. Pine trees do not sprout new growth from bare branch areas. Don't trim off only outer dead needle clusters; remove that entire dead length back to a living lower branch or the main trunk.