You fill in the appropriate part of the V5 with their details. You BOTH sign the V5. YOU are legally responsible for sending the V5 to DVLA. Best sent by recorded post.

Do note that the car tax will immediately and automatically be cancelled, and a refund issued to you. THe new owner will be responsible for taxing the car.

In addition, don't forget to tell your insurance that you no longer own the car, and it is to be taken 'off-risk'

No money changing hands makes no difference.

Just fill in the V5 and away you go. Remind her that he/she has to tax and insure the car from the day of transfer. Your tax gets refunded automatically, you'll have to do the insurance yourself.