There are three basic types of fruit trees to choose from:
Dwarf produces regular-sized fruit on trees 5 - 8' tall. Dwarf trees yield a more manageable amount of fruit for home gardeners. Fruit is easy to pick and the trees are simple to care for. Dwarf trees work well in containers.
Semi-dwarf grows to about 15' if not pruned or trained. The fruit yield is comparable to a standard fruit tree and you probably need a ladder to pick it.
Standard are full-sized trees like the one you climbed on when you were a kid. Because of their size and extensive root system, they can grow quite large and produce a lot of fruit.
Without pollination, there would be no fruit. The plant tag should tell you whether the tree is cross-pollinating or self-pollinating.
Cross-pollinating means another variety of the same fruit tree needs to be planted as well. Plant them within 100' of each other to ensure pollination. The bloom periods also need to overlap to be effective.
A self-pollinating or self-fruitful tree is able to pollinate and bear fruit alone, although pollination by another variety will usually increase the fruit yield and quality.
Plant fruit trees as you would any tree or shrub. Keep adequate spacing between them to allow air to circulate - prevent pests and disease.
If it's fruit you want, make sure the tree you select is not a purely ornamental one, such as some cultivars of pear, cherry and plum.
Some out-of-the-mainstream fruits such as avocado, persimmon, olive, paw-paw, pomegranate and banana can make interesting specimens and provide food. Many varieties of nut trees adapt well to the home landscape. Look for regional favorites such as pecan, pistachio, English walnut, black walnut and almond.
A note on growing new plants from seed you collect from your own fruit: It's fun (a great project for children), but don't expect the resulting plant and fruit to be the same as the one you got the seed from. Like any grafted or hybridized plant, when a seed is planted the resulting plant will likely show traits of both the "parent" plants.
Most state's Cooperative Extension Service agencies have lots of great information on growing fruit for home use. Take advantage of this valuable local asset.