The primary problem with this tree is that it lacks a strong central leader. The tree has far too many lateral shoots that are producing upward growing shoots (photo at left). The first step in pruning this tree is to identify the shoot you wish to promote as a central leader. The shoot I would choose is identified by a red arrow. Since my goal is to stimulate the central leader, my next step would be to remove the leader's closest competitor (yellow arrow). Take this limb off all the way back to the trunk. Next, start making bench cuts on all other lateral branches. I've pointed out just one of these cuts in the photo, but many more bench cuts should be made to remove all upward growing shoots on lateral branches. Keep in mind that you should limit the amount of wood removed during dormant pruning. Only cut what is necessary to stimulate the growth of the central leader. Excessive dormant pruning leads to uncontrollable regrowth most often in a strongly upward direction (this is how this tree developed so many upward growing laterals in the first place). The dormant pruning cuts made on this tree should be followed up by directive summer pruning cuts made as spring growth emerges. Summer pruning has proven to be the most effective way to define and keep a strong central leader in the long run.
In the first photo of pruning this tree, I pointed to a limb that needed pruning to release the leader to grow more vigorously. In the second pruning photo, the yellow arrow points to the same limb that needs removal back to the trunk. From this photo angle, you can see just how competitive that limb is towards the central leader and why it needs to be pruned out. Also, the green arrow points to a fork in the central leader. One half of that folk needs to be removed before it grows into a more difficult pruning problem.