How do you ask a friend for a pad or tampon?

You simply ask them: "Hey, can you give me a tampon/pad"

It's that easy, it's no different to asking for a breath mint or a pen in class. Menstruation isn't some secret you've got to hide from the world, if you're female then you likely menstruate and your friends know that. There's no reason to scream it from the rooftops, but no reason to be secretive about it either.