What percentage of each transaction does visa get?

It depends on your volume and who you sign up through ie: a bank, or other vendor. Usually it ends up being 2-5%. Visa and MC also charge extra fees for many other things. You will be charged extra if you manually enter a card number instead of swiping it, if you don't settle at the end of every day, if a customer uses a Corporate card, etc. Debit cards have different fees. Discover does not charge the extra fees.

Correction:

Visa and MasterCard are just the 'networks' over which the cards are issued under. For a typical debit card transactions with a signature for $20. Visa would only make $.0395. The bank that issued the card would receive approximately .$36 and the credit card processor would get about $.10.