You talk to a psychiatrist about what's been going on in your life. It's like a normal conversation (that is, awkward).
They will probably test things like how good you are at remembering things. They may do an IQ test, a personality test (a test that asks you questions about yourself), or an achievement test (reading, math, etc.).
They will ask about problems in school, and they will try to talk to your parents about your early life. If they can't talk to your parents, they'll ask you.
They'll also be watching your behavior, like your body posture, whether you make eye contact, how you speak. Try not to be too self conscious (and anyways, they know that anybody going through testing is going to be a bit self-conscious anyhow).
You'll have to wait a while after the testing to get any answers. They have to process the tests and things.
If it turns out you have autistic traits, they'll try to tell whether they come from autism, or something similar like being very introverted, having social anxiety disorder, being socially isolated by circumstances, or having some other psychological or neurological condition like depression or ADHD. If your autistic traits aren't due to anything else, then they'll determine whether they are strong enough for a diagnosis. Usually the question is something like, "Is this person impaired in any major area of life?" If the answer is yes, then you'll get a diagnosis; if not, you may get something like "sub-clinical autistic traits", which isn't a diagnosis but could help a counselor figure out how to help you with life issues, if you are going to see one.