It might be different in your area, but my assessment happened in two parts.
The first appointment was an unstructured interview, where I basically just chatted to the assessor for 2 hours. He asked questions about various subject related to aspergers (various traits and such), about my childhood and family, my career and education, mental health history etc. Finally we talked about how a diagnosis might affect me.
The second part was an ADOS assessment (with a different person), which is a structured assessment with activities and questions. Activities included: telling a story from a picture book, miming brushing my teeth, choosing a few objects and making up a story with them. Subjects discussed included: emotions, organisation and planning abilities, stimming, interests and so on, basically all the traits indicative of autism were covered. During this process the assessor also pays close attention to body language, facial expression, conversational abilities and so on.
My advise is:
Firstly, go armed with a list of traits you identify with to be sure that everything is covered.
Secondly, try not to worry about it. The assessors will expect you to be anxious and will do their best to help you be at ease, it was quite a relaxed and informal process in my experience, and really nothing to stress about. This is one situation where you really don't have to worry about seeming odd or awkward. I tried to think of it as an opportunity to truly be myself without any pretence (although it is very difficult to 'drop the mask').
I hope it goes well for you and you find it to be an enlightening experience, whatever the result