You can have a customer Purchase a Gift Certificate or you can send a Gift Certificate to the customer from the Admin in the Gift Certificate/Coupons ... Mail Gift Certificate ...

Then the Customer would need to redeem the Gift Certificate from either:

1 the link in the email

2 the Gift Certificate FAQ in the Information sidebox

3 on the checkout_payment page during checkout and then they need to Apply the amount to use on the checkout_payment page

There is not a built in way to apply an amount to the Customer's Gift Certificate Balance in any other manner, at this time ...