The place I went to previously employed the stylists. You paid at a front desk and they took the tips and put them in an envelope with the stylists name and your name so they knew where the tip came from.
Last week I went to a new salon. There are only 3 women who work in the shop. All 3 own the salon together. Each one has their own I-Pad and when you are ready to pay, the stylist pulls out her I-Pad, connects a scanning device to it and runs your credit card through the device. A screen pops up and you pick a percentage of the tip you want to give them or you can enter a different amount. You sign the I-Pad and done.
Some places prefer tips be paid in cash even if you pay for the service with a card. The woman who did my hair said they prefer to deal only with credit cards or checks so they don't have to worry about cash in the salon.