The period between my self-diagnosis and making it official was very brief (under two weeks), but I did tell my parents and siblings in that interim. I showed them the results of online self-tests, like
RidingDutchman suggested, and I would have also presented the table that
Mia shared, if I had known about it at the time. Back-up is always helpful!
It may be wiser to keep your suspicions to a very limited number of people at first, sort of like
Judge recommends. Self-diagnosis is very common among autistic adults, but most NTs won't understand that this is acceptable in spectrum culture. There is a lot of skepticism about self-diagnosis of any identified medical condition these days, as the rise of sites like WebMD have made many people into armchair self-diagnosticians. (They're wrong about as often as they're right.)
For the people you
do tell, you might want to explain that Asperger's often goes unidentified for many years if it isn't recognized in childhood, and that the disorder wasn't listed in diagnostic manuals until 1994, after you were past that early window. You might also include that it can get harder to identify in adulthood because we learn to adapt over time, making traits less evident.
You should definitely say that you've done a
lot of research on the subject, that you've consulted with others who are either diagnosed or identify as Aspies, and that you see yourself fitting the Aspie shoe very well. You could mention that the stereotypes about Asperger's are no more applicable to all Aspies as stereotypes of any other group are to them (a handy example would be helpful; Black people, gay people, whatever your audience would understand and accept).
Finally, you might mention that diagnosis by a doctor can be a lengthy process, and that you're only telling people close to you right
now because you're learning to accept the likelihood that you are indeed on the spectrum and would appreciate their support.
Be prepared to answer questions and concerns with facts, and an assertion that
this is okay with you -- an answer to a very old question, or many of them. If you make your disclosure with a question in your voice, people will perceive that and likely be less confident in your assessment. And of course, your general attitude about having Asperger's will help shape the attitudes of those you choose to inform (though like Judge said, you can never be sure about reactions).
This is what has worked very well for me. I am open about my AS and have had very little resistance from anyone I've told. I hope you find what works for you.
I wish you well with your journey on this!