Plant a tree on a dwarfing rootstock which has 3-7 weak, short branches (feathers) about 30 inches up the truck. Any branches which are too strong should be cut off at the trunk. Try to leave a whorl of feathers at about 30 inches. If there are no feathered trees a whip (a tree with no branches, or you can cut off branches which are too strong to make a whip) may be planted and headed back (cut off) at 5 feet to encourage weak growth at about the 30 inch level.
A 2-3 inch treated pole stake should be driven 2 feet into the ground about 6 inches from the trunk of the tree. Other types of stakes or a trellis may be used instead. Cut the trunk at 8 to 10 inches above the bottom whirl of branches, which should be about 24-30 inches from the ground.
Tie any branches longer than 10 inches so the tip is lower than horizontal.
When the leader (the top branch that grows up) starts to grow bend it at a 45 degree angle. You can tie it to a lower branch or to the stake to bend the top down.
After the tree has reached the desired height, each year cut one or two branches in the upper part of the tree back to within a few inches from the truck with an angled cut that faces upward (sometimes referred to as a dutch cut) to encourage new, weak growth. Controlling the vigor of the upper part of the tree is critical.
Principles of training apple and pear trees.
Don’t cut one year old wood. It’s the shiny wood at the end and it can be short or long. If you cut it it will grow a lot more branches but if you leave it it will form fruiting spurs. If you have to cut one year wood on a branch cut it all off go into the two year old wood or just cut it all off to the branch it grew from.
Angle of the branch. If a branch is weak you want to bring the tip up higher to make it grow faster. If a branch is too strong you want to pull it down so it is more horizontal to slow it down. The more upright the branch is the more vigorous it will be.
Here is a wonderful video by Tom Thornton on summer training of apples.
Here is an article from Cloud Mountain Farm on apple pruning.