How would you go about getting an autism diagnosis for a young adult? Is there any benefit to get a diagnosis?

Find an expert. In most areas, it would be highly unusual for someone with autism to make it to adulthood without having been diagnosed, but it still happens. Evidence suggests autism manifests between birth and age 21/2 or so. There is no specific treatment for it; but, knowing what the trouble is may help. Also, am autism diagnosis might give eligibility to programs & services restricted to that diagnosis.
Need to be seen. By a practitioner qualified to diagnose autism in adults. There is a benefit to having the diagnosis if it gets you the help and therapies you need to succeed. It may also help explain many symptoms you have had through the years. Many adults have aspergers, not autism. So yes there is a benefit.