Asperger's Syndrome is considered to be a high functioning form of Autism where social behavior is impaired yet other areas of functioning (such as intelligence) are average or above average.
Within the AS community, there are people with formal diagnoses, and those with informal or "self" diagnoses. Diagnosis as an adult can be difficult. Many adults will have multiple psychiatric labels prior to a diagnosis. Commonly, these include depression, anxiety, bipolar II, schizophrenia, social phobia. It may be the experience that the previous diagnosis does not quite "fit", but it is a sad fact that many AS adults have psychiatric comorbidities alongside their AS. There are pros and cons of a diagnosis as an adult. The biggest advantage appears to be that people suddenly feel they have an answer to the puzzle "why am I different?" It can also help the person find appropriate coping strategies - my own experience was that understanding my AS allowed me to work on ways of reducing my sensory overloading. The big disadvantage of a formal diagnosis is if it can lead do discrimination. High functioning individuals may be very reluctant to have a formal label, as it may have implications on how employers treat them.
It is important you are seen by a specialist who is experienced in the diagnosis of AS in adults. You may need to ask around to find out where your nearest adult diagnosis centre is. Some require referrals from a family doctor, others accept self-referral. In adults, because coping strategies are learned and can conceal certain aspects of AS, there may be a need to provide information from family members who knew the person as a young child.
Many people are satisfied with an informal diagnosis. One popular quiz is the aspie quiz. This also has links to a number of other testing resources.
The Autism Research Centre in the Uk has some very good tests for free that include things like reading facial expressions and such.