A wide variety of competitions can be found at the local level in clubs or sponsored by local organizations.
Schedules for these competitions can be found by contacting your division, or visiting askfred.net (the registration platform for local tournaments). You will need a membership through usafencing.org before activating a profile on askfred.net. The two platforms do not "speak" to each other, as they are two separate databases so creating a profile and membership at usafencing.org as well as creating a profile for registering for a tournament are needed.
Division contact information is available by emailing information@usafencing.org.