A quick google led to this

Here's how to prune nectarine trees.

Nectarines are a great substitute for peaches. The main difference between nectarines and peaches is the skin texture. Nectarines have a smooth skin while peaches are sort of fuzzy. Because of the smooth skin, nectarines appear more reddish as compared to peaches. Early pruning is very important to maintaining healthy nectarine trees. When pruning nectarine trees, it's important to remove the previous year's growth, as well as any branches that are dead, damaged or diseased. Pruning the inner branches of the tree helps open it up to more sun light and better growth [source: URI]. Here's how to prune nectarine trees.

1. Prune nectarine trees lightly at the beginning of the summer.
2. Prune away any diagonally crossing limbs that are rubbing against other limbs. All new growth that appears weak should be pruned away.
3. Prune away any dead, damaged or diseased branches, as mentioned above.
4. Stagger the branches. Cut the branches back to different lengths to encourage new fruiting wood to form throughout the crown, not just on the tips of the branches. For example, cut them by staggering the branches thus: the first by ¼ inch, the next by 1/3 inch, and the next 2/3 inch back.
5. Remove any shoots that start growing up the tree's center, to keep the area around the main trunk fairly open.
6. Make your pruning cuts at an angle.
7. Remove all debris and cuttings from around the tree

Thanks, these trees were volunteers that grew out of my compost heap. I have a 3rd tree which is a little over 2 years, but seems to be diseased or full of borers with sap coming out of little holes. On these 2 trees, do you see any major branches I should cut out?

Cut the suckers that are growing out of the ground in the top pic.

I'd take out at least half of those trees. Open them up to more of a vase shape. That means taking out the center, big, upright wood. Remove part of the remaining big branches to shorten them. Remove any wood hanging down below the remaining main scaffolds.

This will cause a lot of new fruiting wood to grow this summer and produce next summer. After that remove about 1/3 of the fruiting wood each spring to keep the tree size down. You also will probably need to remove the strongest growth this summer. If you prune as hard as I'm suggesting there will be very strong regrowth this summer. Don't let that get too big.

Here is a closer up picture of the first tree. Would you remove the whole middle branch or cut above the v shape?

From what I see in the above pic, your tree has a good vase shape. Personally I would focus on removing branches that are less than 1/2" diameter. If still crowded looking, you can remove 1" dia and less, plus any crossing branches growing sideways not up. The link I posted had the details but If you don't relate, YouTube "pruning stone fruit trees" and you'll see good examples.

You won't be wrong taking out the whole center of that tree. Your tree has massive vigor. It will regrow even if you make a mistake. Shape it the way you want after that. Peaches and nectarine need more pruning than almost any other fruit tree. Removing 1/3 each yr isn't too much. They fruit on last yrs wood. The best fruit is on last yrs shoots that are 18-24 inches long. Prune enough that you are getting lots of shoots that size each yr.

Currently your tree doesn't have many last yrs shoots that size because it has too many shoots.

I'd also want a lower tree. You can only get that via major pruning.