Nuts store very well by properly drying and storing in air-tight containers in a cool location. Refrigerated (at 32-45°F) nuts will maintain quality for one year and frozen (at 0°F) nuts will maintain quality for 1, 2, or even 3 years depending on the type of nut. The University of California has more specific information about harvesting and storing different types of nuts.
It is no longer recommended to can dry nuts alone. This is due to risk of condensation from the canning process leading to bacterial growth. A better option is to vacuum pack dry, shelled nuts.
Smaller quantities of nuts can be used in a jam-like product called conserves. Here are some ideas to make and preserve these at home from the University of Georgia National Center for Home Food Preservation.