First, get prepared. I'd recommend downloading and taking with you a copy of the Washington OC pamphlet. Get a pocket recorder and carry it.
Second, baby steps. Start out by going to OC meets and OCing in OC friendly places like Starbucks and Walmart were they have overt policies in that regard.
Third, you can ease into by carrying is a semi open style. Because I ride a motorcycle, I wear a jacket that drapes over my sidearm but doesn't cover it completely.
Last, remember that your people skills play a part in how it all goes down. Many times a friendly hello and a smile has made a visibly uncomfortable person relax.