Eastern Washington consists of a much dryer landscape than that of western Washington on the other side of the Cascades. Some common wild trees found in this area are evergreens such as the ponderosa pine, lodgepole pine, western larch and deciduous trees such as the black cottonwood, Oregon white oak and trembling aspen. Especially if you have never identified any trees before, take a regional field guide with you for reference as you explore the forests of Eastern Washington.
Pack your field guides with a camera or a notebook if prefer sketching for when you want to go out and identify wild trees. In Washington, the field guide pamphlet "Washington Trees & Wildflowers: An Introduction to Familiar Species" is great resource because it outlines the most common species you are likely to encounter. If you don't mind carrying it, "The Sibley Guide to Trees" is an indispensable resource when identifying trees anywhere in the Unites States.
Observe the leaves of the tree to determine if it is deciduous or evergreen. Deciduous trees such as oak, maple and birch have leaves that fall off every fall and grow anew in spring. Evergreens usually have needles, such as pines, spruces, hemlocks and larch. This will be the most obvious and first thing to note about a tree which you are trying to identify. If it has leaves, note the shape and size. If it has needles, note if they are flat or round and how long they are. Note if they are in compact clusters or loose sprays. Every detail will help to narrow down the possibilities of what it could be.
Note the characteristics of the bark--the color, whether it is scaly and rough or smooth, whether pieces of it flake or peel off or is tight. All of these will help you to compare species that may look similar in other ways but have different bark.
Note what kind of environment you found the tree in-- in the woods, on the edge of a field, near a stream, on the ridge of a mountain.
Note the overall size and shape of the tree. Approximate how tall you think it is, since it is unlikely you will be able to measure it. Lodgepole pines grow to about 80 feet, while Douglas fir--also an evergreen--can grow to 200 feet.
Take a picture of the tree, or sketch it if you want. This helps when you don't have a field guide with you so you can compare to pictures in your books at home, or if the guide you are carrying doesn't seem to have anything that matches up.