If it were *my* tree I would cut the trunk right where that white tag is tied on. Then I'd cut the remaining 5 branches at about the same hight as the trunk cut, selecting spots to cut where there are buds remaining that will go outwards and/or sideways. I want that tree to be bushy and low. I do not want long whippy branches like I see in the picture. You would then likely get furious branching growth in every direction with this sort of pruning. Maybe that's not what you want, I don't know.

You didn't mention what rootstock this tree has or what sort of size you're ultimately looking for.

Off the top of my head, I remember ordering a 'Supreme Dwarf' tree. Records are at home.

Don't want it tooooo tall. If I need a ladder eventually, that's fine.

tc, with the prunning you would do, how long before it would bear fruit? Like I mentioned, It grew fairly well last year. Do I want fruit this year?

sheila

I wouldn't want fruit off of that tree this year, or even next. Look at those branches, they're going to bloom all the way to the top. What would happen to those branches bearing fruit?
I prefer an open-centered tree, even for apples, your mileage may vary and you'll certainly find various opinions about that. Looking again I'd be a bit more conservative and not cut it quite so low. You can always cut out the upper portions of the tree as it gets larger. But I would still cut all of last year's growth back to a couple of buds. This will encourage branching, possibly too much. You can always knock off buds that branch in unwanted directions. Look down low at the base of each branch. Look for buds on the outside and on the sides. Pick the location of the cut that will leave these buds that will form branches going outwards from the tree, not inwards.

A couple of tips:
In your picture I can see some dead wood stubs where a pruning cut was made too far from the growing bud. This leaves a bid of dead wood that will never heal over. Like at the bottom of the lower right branch in your picture. Snip these off and in the future make cuts closer to the bud, but not *too* close. If you're conservative, you can always cut off the excess later after the bud grows. Sometimes cutting too close to the bud can kill it. Leave about 1/16 - 1/8 of an inch beyond the bud your cutting back to.
Also, I can't see the graft union in your picture. This is where the rootstock is grafted to the main tree. I suspect it's under that pile of mulch. Make sure that it's uncovered and exposed to air only, otherwise roots will grow from the main tree and will totally defeat the dwarfing rootstock. Which means your tree will grow alot more vigorously.

See that very topmost vertical shoot? Take it out just above the crotch for the second branch and even with it. Make a nice clean, fairly close cut. What you want is for that second from the top branch to become your Central Leader. The reason for this is if you leave that highest shoot for a CL it will really take off. The tree will quickly grow too tall in relation to the bottom. I do this the middle to last week of June. This takes practice to determine when to do it in regards to your climate and ground. Do not dormant prune this tree. In fact don't do any more pruning on this tree than this one cut. Just tie the limbs down to a forty-five degree angle, all of them. At my location around the Fourth of July I would head all side branches about one-third. When you tie them down you will have buds break vertically to form what are called "risers". It is best to rub these out with your hand when they are only a few inches tall. Some people leave them and head them back the following summer. You can try both ways to see what you prefer.
What I have described is known as a "French Axe". You want it to look like a Christmas tree with many branches, but the ones on the bottom longer than the ones on top; pyramidal. And take TC's advice on exposing that graft union. If this is my tree and it is a dwarf I would drive a stake beside it.

Gentlemen, thanks you for the help. I will follow your advice.

Geraldo, one thing though. Again, I purchased it from Starks Bros, and in their 'How to grow fruit trees' booklet they give you, the recommend that the tree should be pruned in "every dormant season" ?!?

Yet you say 'don't dormant prune this tree'. Why?

When do you think is the best time??

Thanks again for your help.

sheila

Stark Bros. sells fruit trees and for them the worst thing that can happen is that their trees fail to grow for their customers. You dormant prune a tree to make it grow up. Keep cutting those branches back one half to one third of last season's growth, in the dormant stage, and the tree will keep extending branches and growing. When you stop pruning, the branches will set a terminal bud and the tree will move from the vegetative state to a more fruit producing state. It will still grow, but it will tend toward slower growth with more fruit production.
I want a fruit tree to produce fruit as soon as possible. People go to much expense to produce and buy nursery fruit trees with branches. Those branches are called "feathers". Those feathers will have apples the second year you own the tree.
Actually, I don't hardly summer or winter prune an apple tree until it reaches the size that I want and it begins to have fruit; then I start pruning it using a little summer pruning and little winter pruning. One thing I do at that time is to cut the scaffolds back into the two or three year old wood in order to stiffen those limbs. We use to call this "mold and hold".
This is my way and others have other methods. TC is describing a method called the Open Vase system. This is the older way of pruning an apple tree and I think it is still the preferred method for a tree which is on a large, vigorous growing root. It puts more light into the center of a big tree. You mentioned that your tree is a supreme dwarf. I would take that to mean M9. My preference for that is the French Axe.
I planted my first Grannies exactly thirty years ago and they were on M7. Those trees easily reached fourteen feet tall.