I've gotten more than a few women into shooting. Some just can't get into it. So if you have a wife or girlfriend, don't pressure them into it. You put pressure on them and they will just refuse to come or if they do go shooting, won't have any fun doing it. I've also found more than a few girls who just can't stand the thought of killing something with a firearm so I generally keep hunting talk or pictures out of the shooting experience. Some have gotten over this and want to hunt, others have not.
Some women want to be alone with you for their first time shooting so they won't be embarrassed, others need to be in a group to build up courage. If they want to be alone take them out into the woods (less chance of people watching which might make her nervous). Some women though need to be in a group so other women can encourage them. In this case it always helps to bring in a woman who knows how to shoot and will use larger caliber guns. A lot of women in a group feel that if one can do it, so can they.
Start small. Usually a .22LR. This works for both pistols and rifles. Allow them to shoot that until they are calm with it. Do not rush them. If it takes multiple trips then so be it. When they are calm then politely offer to bring something larger. Once again do not force them into something larger.
Use lots of encouragement.
Start with a paper target to help them learn to aim. Then once she can aim switch to reactive targets. The more reactive the better. The best paper targets are the shoot N See targets (holes change color). Reactive targets can be pop cans, golf balls, anything that makes a noise and moves when shot.
Then move onto something slightly larger. .223 works well as does .410 if they want to get into shotguns.
Some will immediately hate anything larger than a .22LR. If that's the case oh well. She either wasn't ready for centerfire or she's just wants to shoot rimfire. Don't be disappointed.
After using a small centerfire until she's comfortable then you offer something in a larger caliber.
Remember, don't talk about things that might scare someone from shooting. Don't brag or joke about the amount of recoil a certain gun has or how much it hurt your shoulder. That may worry them and so they won't move up to a larger caliber.