How do I know about being tested for autism or aspergers?

Depends on age. Testing for these disorders involves a combinatio of questions to parents and teachers plus some direct psychological assessment of the child or adult. There are no established laboratory tests for making the diagnosis. Some of the questions are easy to misunderstand or overinterpret, so it it important to work with someone with experience in diagnosing autism.
Aspergers. Best thing to do is find a good licensed psychologist who works with adults. Typical assessment involves interview and a good developmental history. This is how it's done for children and teens. and this is an overview of aspergers.