Both deciduous and evergreen trees can be grown in home gardens. Identifying a tree in your garden will take some work on your part, but there are several resources to help you. The pocket field guide from the Arbor Day Foundation titled "What Tree is That?" is a useful resource, as is the online version of the guide. Trees are perhaps best identified by the characteristics of their leaves.
Simple leaves are leaves that grow singularly from a leafstem. Simple leaves can either grow opposite each other on a stem or alternately from one another. Maples are examples of trees with simple leaves that grow opposite each other. Birches and willows are examples of trees with leaves that grow in an alternate pattern.
If your tree has multiple leaves on each leafstem it has what are called compound leaves. Unlike simple leaves, compound leaves appear in multiples on a single stem. Like simple leaves, however, they can also grow in an opposite or alternating pattern on the stem. Ash have compound leaves. Determining whether your tree has simple or compound leaves is a first step to identifying your tree.
Leaf margins refer to the edges of leaves. Leaf margins can be smooth. However, they can also be fine toothed and double toothed, giving them a serrated edge. Some trees have leaves with rounded teeth called crenate margins. Leaf margins can also be lobed. Oak leaves are examples of lobed leaves. The unique leaf margin of your tree will aid you in identifying your plant. Pick a leaf from the tree, or bring your guide book with you into the garden, and compare your leaf to the book's pictures.
Trees with needles are called conifers. Conifer leaves are easily identified by their needle-like shape. You will need to know how many needles are in a cluster, as well as the cluster's pattern to identify your tree by its needles. Conifers can be both deciduous and evergreen. Knowing whether or not your tree sheds or keeps its needles during the winter will help you identify your tree.
You may think of all tree leaves as being green, but in fact many come in various shades of green, yellow, blue and even red. Spruce tree needles, for example, often have a blueish tint to them. If your tree leaf is a unique color this will help you identify your tree more quickly. In general, any unique features you can note on your tree's leaf will assist you in identification.