One usually would say give a massage or get a massage

I agree with the previous answers. You "get" or (more formal) "receive" a massage. You "give" a massage. But you can also say "perform" a massage.

Ah - I didn't see the answer box as opposed to the comment. To repeat it I suppose - you give a massage, you don't do or make it. Saying do or make a massage would sound very strange indeed (though maybe that's just me?).

*massage - saying either do a massage or make a massage would definitely make me laugh.