Summarize this article:

Snipping off new growth helps make sure that all of the tree’s branches are getting enough light. Heading off fresh branches early will train your tree to keep growing in the proper structure and will lessen the number of large branches that need to be removed later, once they start causing problems. If a branch breaks because of heavy winds or because it’s bearing a lot of heavy fruit, remove it as soon as possible. Make the edges of the break clean by cutting away any jagged or broken pieces to promote healthy, quick healing. This process helps prevent the tree from over-producing, and improves fruit color and health throughout the tree.  Keep an eye out for boughs that are producing a lot of apricots and becoming too weighed down, and cut away some of the branches to prevent breakage. If your apricot tree is only producing a substantial apricot crop every other year, thinning out fruit branches on heavy years helps to correct the tree and encourage it to produce a consistent crop every year.

Summary:
Remove small sprouts a couple of times during the summer. Cut off any new branches growing towards the trunk or other branches. Prune away damaged branches immediately. Thin out fruit-producing branches in early summer, when apricots are about one inch.