Depending on where you live, it could be as simple as going to the store and buying one and arranging for a lesson at your local shooting range. It helps if you have a knowledgable friend. What state are you in? And what kind of gun (rifle, pistol, shotgun) are you interested in?
The 85th amendment provides a clause for this, but it requires video footage made available for review.
Ask around. Find a reputable dealer that several people recommend. If all else fails, go down to your local police station and ask them to recommend a gun safety course. At my old agency, these questions were always directed to me, and more often than not, I taught the people personally...for free.
Washington is a "shall issue" state. If you buy a handgun, you can get a concealed carry permit. You cannot be refused a permit unless you've done something that disqualifies you.
I don't have the program name handy, but the NRA has a women's shooting program--possibly "Women on Target"--that can probably help you out if you are a complete newbie. [edit: Yup. It's "Women on Target".] [edit-edit: Sadly, it doesn't look like they have any clinics in Washington. ]
Women are better shots than men in general. When people try to teach them, they actually listen. Guys figure that they already know how to shoot by nature of their gender, so they don't pay as much attention to instructors.
