Men or women, the trick is to get them out for a shoot and make it a positive experience for them. Beyond that there is no magic - I've done it countless times.
Once exposed to, say, handgun shooting (or any shooting for that matter) the person will fall into one of three categories:
1. Hated it - no further interest. At least with this situation you can still instill in them a basic respect for your interest in it (i.e. they are not personally interested in shooting, but are also less or not interested in seeing you prevented from owning guns and continuing to shoot). I've softened a few "gun haters" this way.
2. Liked it - even surprised themselves (but not enought to pursue it). Maybe want to go out again.
3. Liked it and willing to pursue it by actually getting licensed and buying and shooting their own guns.
It's clearly in our interest to take people who've never shot and turn them into 1s; and to turn the 1s into 2s; and to turn the 2s into 3s; and to get the 3s to start this cycle all over again with the people that they have contact with.