Especially for young trees just planted last year, late winter and early spring is an essential time to prune. As trees are dormant, not yet growing, this is usually called "dormant pruning."
If you remember nothing else, keep in mind the 2 C's and 3 D's. Remove any crossed and crowded branches, and any dead, diseased, or damaged. Crossing branches rub on each other, wounding bark and allowing diseases to enter. Crowded branches keep light from getting to the inside, so you won't get as many leaves and fruit, and may get more diseases instead. For older trees, the adage is that a bird should be able to fly through the tree without interference.
Dead branches are obvious in the growing season, but this time of year with no leaves you'll need to look for ones off-colored, often with shrunken (canker disease) areas. When pruning damaged branches, prune back to just above a bud, to a lower branch, or back to the trunk. Where older branches come off the trunk they form a raised area or ridge of bark. Cut back to, but not into, this bark ridge or "collar."
Another important point with many fruit trees is the branch angle, as measured at the base, from the trunk. Those mostly horizontal, usually a bit under 90 degrees from the trunk (a right angle), are the strongest and bear the most fruit. Those upright, especially at an angle less than 45 degrees from the trunk forming a V-shape, have what are called narrow crotches (where the branch meets the trunk). These are are vigorous, produce less fruit, and are prone to breaking in wind and winter ice. Branch angles even may vary among cultivars of a fruit type, such as Delicious apples growing more upright, and Jonathan being more spreading.
You have a couple options for such branches, one being to prune them off at the trunk. If the tree is young, and the branches are where you'd like them, they can be "spread". If real young, only a few inches long, push them downward using a clothespin clamped on the trunk. If they're a bit longer, even a year or two old, hold them downward for a season with wood stakes (with a cut off nail on each in), or by hanging weights (fishing weights for small branches, cement weights the size of small drink cups for larger branches).
There are three main pruning systems that are used for fruit trees-- the central leader, modified leader, and open center or vase shape. The central leader is just that--one main branch reaching upward, the tree forming a conical or Christmas-tree shape. It is often used for upright trees that don't get too tall like dwarf or even semi-dwarf apples, or European pears and plums. If you don't mind standard size fruit and nut trees reaching a full height, often 30 to 50 feet (more for most nuts), then the central leader system is for you, or rather them.
On the other hand, if you want to keep upright trees such as many apples, upright sour cherry cultivars, and European plums (some of the latter are hardy into USDA zone 5) lower, then prune these to the modified leader. This is like a central leader early in life then, when at the height you want, prune out the main leader and allow main side branches ("scaffolds") to develop.
When selecting which scaffolds to leave, they should be equally spaced around the tree, none directly and closely above another. For dwarf trees, as you measure up the trunk, scaffolds should be about a foot apart, about two feet apart for standard trees, a distance in between for semi-dwarfs.
For some trees you may want to use a variation of the modified leader-- the multiple leader system. It is a cross between the modified and the central leader. Once the tree is tall enough for you to manage or as you desire, prune out the leader but allow several upright (not horizontal) branches to develop. This is often used for European pears; in case the fireblight disease attacks one or more leaders, there will be others left.
The final system is the open center or vase-- descriptive of the shape. This is used for spreading trees such as peaches (where they can be grown, most aren't hardy even into zone 5), filberts, spreading sour cherry cultivars, and American plum hybrids and their species. For an open center, to allow full light to enter the center, don't let a central leader develop. From an early age of the tree, prune to have 3 to 5 main scaffold branches. Then each year in late winter or early spring, prune off any upright shoots in the center of the tree. Prune upright shoots farther out on the scaffolds back to a bud pointing outward. This will keep the tree growing more horizontal then vertical.
A couple other rules are useful when pruning fruit trees. The more you cut off, the more growth this stimulates. So if you want to slow down growth on a vigorous tree, don't prune it as much. Pruning in summer can help this way too, as pruning then results in less regrowth than dormant pruning. Just don't prune after midsummer, so any new growth can harden by fall.