It's relatively easy to run fuzzing for a headless application. A headless application doesn't have any GUI, and can be simply run in a terminal. You can use your favorite fuzzer, and feed fuzzed data to the application. Normally, a headless application just processes data, and then quits or crashes right away. But it may be a little different if you are trying to run fuzzing for an application with GUI. This blog post explains how to run fuzzing for AbiWord - an open source text editor.
Read more about Fuzzing GUI applications