If your dreams include shooting in the Olympic Games, you'll need to join USAS so you can take part in their sanctioned events. Start with local matches, and then you can progress to regional and national competitions. Top scoring shooters who are also citizens of the USA can work their way to the top, and if you meet the requirements of the International Olympic Committee (IOC), the United States Olympic Committee (USOC), and the International Shooting Sport Federation (ISSF), you may be selected for the US Shooting Team (USST).
If your expectations are a bit more modest, just ask around at your local range about where to find and join in some shooting competitions, and go from there.

