Everybody loves a young fruit tree, but for those of us who are a bit more matronly, keeping in shape can be a challenge. Taking your tree from an shocking mess to full fruited glory isn’t hard, it just takes time. But hey – what’s a few years of your life when it’s for a tree? 
Before you get started, be aware that this will take three to four years, depending on the condition of the tree. Since this is no small task and many dwarf trees would give you fruit in three years, ask yourself if renovating the old one is worth it, or if planting a new one is better.
Apple and pear trees are most easily renovated. Cherries also, but with less success. Peaches and nectarines don’t renovate well.
New is not always better – I love those old trees. Their bark is corky, their form funky; those branches have stood through history, good and bad. Maybe the old gal has luscious, old-fashioned fruit, or sentimental value. Whatever your reasons, take our time with your tree, and follow these simple steps.
Let there be light: clear away any competing trees and brush, to get rid of shade. But if the tree’s in a shady spot, cut out competing plants over two years to reduce stress from too much sun all at once.
Body check: look for soundness. Are the trunk and main limbs healthy enough to bear the weight of fruit? Is it diseased? Examine the trunk and ends of the major branches. They should be reasonably solid, with little deadwood. Don’t worry if parts of the trunk and main limbs are nonfunctioning – they give strength to the tree.
But if they’re hollow, saving that tree is an exercise in futility. Then get pruning:
Step 1: prune out all broken and dead branches and cut away the sucker growth around the bottom of the trunk. 
Step 2: decide how big you want the tree to be. Realize, however, that you can never make a giant tree into a dwarf no matter how much you chop – you are not Edward Scissorhands. Old trees can be maintained at 10 to 16 feet (semi dwarf) and 16 to 20 feet tall (standards).
Trees that haven’t been pruned in a long time should NOT be reduced to the desired height in a single pruning. To prevent rampant growth and damaging sunburn, reduce height over three years by removing no more than one-third of the tree in one season.
After you decide on the desired height and limb spread, look at the major branches to determine where they could be cut to bring the tree into that shape. Reduce tree size by cutting back branches to those growing more horizontal to the ground, thinning out excessive branches, or those that cross or rub against others.
Flag your choices for removal with colored plastic, then step back and look at your choices, imagining how those cuts will effect the tree. Once you begin pruning step back after every branch removal to assess how it looks, adjusting other choices to keep the tree in balance.
Note: do not apply nitrogen after the initial heavy cutting.
During the summer after the first pruning, the tree will produce water spouts (rapidly growing vegetative shoots that develop around pruning cuts). Remove them, but the way you do this is important: pull the shoot off the trunk in mid-June when they’re 10 to 12 inches long. Do this throughout the season. The shoots can be pulled off safely as long as their bases remain tender and green. Stop when the base of the shoot becomes woody and does not easily pull off.
In the next winter, cut back another group of older branches to those growing more horizontally, keeping to one-third of the original numer to be removed. Then thin out the bearing wood. Look for 1- to 4-year-old spurs – the buds where fruit is produced. The best fruit grows on spurs that are 2 to 3 years old. Thin spurs older than this, or cut them back by half.
In the third winter, remove the final branches to horizontal limbs.
I look at your picture of a sucker on the base of a tree, and I don’t see sucker, I see gorgeous textural bark! what Is that tree, and how old is she? (And what’s up with the tendency — maybe it’s just me — to call any fruit tree “she”?
This tree is ripe with history – it’s one of the old apple tree planted circa 1878 in south Boulder. I’m not sure of the variety. Can’t answer your next question, but to me, fruit trees are “she” because they bear fruit (now, now – before you object – yes, there are boy parts involved in this too, but the tree spends more time with the developing fruit and seeds than it does with pollen).