Here’s the Aftercare Advice I've handed out at the Propagation Fair / Scion Exchange:  

Aftercare of your newly grafted fruit tree:

Label your tree & make a backup record.  Before planting keep it cool, shaded, and the roots always moist.  

Within a month after grafting, expect new growth from both rootstock and scion.  

The rootstock will send out suckers during the first year.  Tip-pinch them back to 3 or 4 leaf sets to redirect the energy from the tree’s roots into the scion above.  On the other hand, leave new scion growth untouched, until the longest stem is 6 to 8 inches, normally toward the end of May.  At this point select the best stem to form the main trunk of the new tree.  Pinch out the growing tips of the other scion stems, leaving 5 or 6 leaf sets on each to aid the formation of a strong union; when dormant, cut them to the base of the trunk.  Water your grafted tree weekly through August.  After August, water sparingly so it can harden-off for winter.

What if my graft dies?

If there is no growth coming from the scion, there will usually be sprouts coming from the rootstock.  Allow one of these sprouts to grow as described above.  Keep the rootstock well-watered and fertilized.  You want one shoot to grow as large as possible so you may bud onto it in August.  HOS has a budding workshop at the Arboretum in August; it’s a great time to get help, and scion wood for your bud. Or - you my graft onto that shoot the following dormant season (or bring it back and have us do it).

Training your young tree:

I prefer an open ‘vase-shaped’ tree to a ‘central leader.’  To create an open vase (when dormant), prune your first year scion growth above the bud where you’d like your highest limb.  The 4 or 5 buds below should put on equal growth the following season, forming the branches.  If one single upright shoot had not reached your desired branch height, do not prune it, let it continue growing straight up.  You may treat it as you did the original graft, by tip-pinching any shoots below the terminal (tip) bud and make your branching cut the following winter.  Soil fertility, rootstock, and varietal vigor will determine whether it takes one or two growing seasons to reach your desired branching height.