Hop variety identification can be done the old-fashioned way of comparing pictures of hop cones of known varieties to the unknown. Although this method is not perfect, it is widely used as a starting point. I have a book on hops printed by S.S. Steiner (a major hops supplier) that contains good photos, as well as verbal descriptions, of the cones from various hop varieties. Another method used these days is gas chromatography. Different varieties have distinctive aroma profiles and these can be shown using gas chromatography. This method requires expensive equipment and an extensive profile library to be effective. Another modern method of hop identification involves genetics and is the only real way to tell for sure what variety an unknown sample is. These methods are out of reach to homebrewers and most commercial brewers.
As it turns out, there were not very many hop varieties commercially grown in the U.S. 75 years ago. If the hops really date back that far, you may be able to determine the variety simply by reading historical accounts of what varieties were grown in various regions of the country. Cluster was the most significant hop variety grown in the U.S. until fairly recently. Although it is nice to know what variety is growing in your backyard, the most important thing is that the aroma is pleasant and the bitterness is not coarse (if used for bittering). Using fresh, un-kilned hops is a great way to add aroma to your beer. The best time to use fresh hops is in August and September, immediately after harvest when the cones ripen. Simply pick them, remove foreign matter (such as leaves from the plant, pieces of the vine and insects) and they are ready for use. Hops are never “washed” and commercial producers use air flow as a method to remove small, lightweight debris.
If you want to store the hops and use them in the future, you will need to dry them for storage. This can be difficult since hops do not weigh much, have a high moisture content after harvest and have a low density. This means that you need to dry a large volume to get much yield. Food dehydrators can be used for this, but due to their relatively small size are not very practical. The serious home hop grower typically makes a small hop kiln to dry their crop for storage.