First of all, most women masturbate outside the vagina, at least as their main stimulation. See, there this little thing called the clitoris. It a little wonder gizmo that can do just about everything. Anyway, seriously--I never stop having sex or masturbating on my period. Luckily I have never been with a guy or girl who was bothered by this. But then, everyone I've been with has been very well educated (about the body and sexuality) and very mature and open-minded. Sure, it can be a bit messier but it's not harmful or painful or any more "unsanitary" than any other fluids and juices that are the result of sex. As some others have said here, a woman is often more horny during parts of her period and can have slightly different orgasms.
I think your actual question is a bit confusing and I'm not clear what you are trying to ask, but if I take it literally and describe to you how I achieve orgasm while on my period--not counting "intercourse" (for whatever reason) and trying to fidget with a tampon (also for some strange reason); then I would have to say that I do it the same way as always. My fingers on my clitoris while doing anal sex with my lover. That is and always has been my favorite way to achieve orgasm, period or no period. I would masturbate the same way too. I love my clitoris. It's a handy little friend.
Dude, you cannot do anything like that with a tampon still in unless you want it to get stuck in there and then go to the doctors and have it pulled out which would probably be very embarrassing. You pull the tampon out and do everything how you normally would if you weren't on your period... but it would be messier though.
I am even hornier than usual during some parts of my period. You can stimulate your clit and have a really good orgasm, no matter what is in your vagina. You don't need to stick your fingers inside your vagina in order to orgasm. I am not comfortable with sex during menstruation but I usually masturbate a lot during it. The clitoris gets really big and tingly during this time so it's a release to rub it until I cum.