First year pruning sets the eventual shape of the tree. If your tree is taller than 4-5' above ground, after its planted, trim it down to that height. Pick out the dominant branch that is the most vertical at the top of the tree. This will be your central leader. Thin out the inward growing branches and any branches which are crossing over each other. Trim off the tips of the larger branches to encourage growth. See the diagram for a look at the branches.
Any shoots or branches which come from BELOW the “bud union” should always be pruned – now and in the future. Brand new stems that grow out of the ground, from the root systems are called suckers. If you see them, cut them off at ground level. When the tree matures, suckering usually diminishes.
If your trees set fruit this first year, pick off some of the immature fruits, spacing them about 8" apart on the branches. This will encourage proper ripening, allow the spray to cover well, and improve vegetative vigor. Fruit thinning in the future is also important for the very same reasons. Less is more. If you don’t thin, you will get many more fruits than the tree can handle, resulting in broken branches and small fruits. Don’t be afraid to thin. The resulting fruits will be fuller and much nicer.
In later years, you should continue “shape” your tree. Plum trees are best trained to a modified central leader (uppermost upright limb) or to a vase shape like peaches and nectarines. It does not want to grow straight up like and apple or a pear, so the central leader will become much less dominant. It will want to spread and try to take over your orchard. This is the natural way your plum tree will want to grow. Pruning will keep your tree vigorous, encourage the establishment of fruit buds, and enable you to keep your tree down to a manageable size.
As plums are vigorous growers, you need to prune aggressively. Summer pruning, when the trees are still growing, will help contain the spreading nature of your plum tree. You cannot over-prune a plum tree. So do clean up pruning in the winter, to get rid of broken and dead branches and shape up the tree. Then in July, prune again to maintain a manageable size.