You can sell gift certificates on your site by selling them like a regular product. You'd have to set them up in different denominations, such as $20, $50, etc as each product in your catalog may only have one price. Manual intervention is required though so that the purchaser can receive a gift certificate code that they can provide to the recipient. The recipient would then enter the code during checkout to receive the discount off of their purchase.
To set this up:
Create your gift certificate products. On the products make a note that you will email details on how to redeem the gift certificate.
Once a gift certificate is purchased and you have confirmed payment, create a discount code with a dollar value for the same amount, good for one use only.
IMPORTANT: After creating the discount code, double-check that it is for a dollar amount and good for one use only as you may not edit an existing discount code to correct any mistakes. It is also recommended that you randomly choose the code as sequential discount codes can be guessed by previous customers.
Email the customer the discount code that they can then pass on to their recipient.
Optionally you may keep a spreadsheet to track your gift certificates sold, the corresponding discount codes, and which orders used the certificate codes. This would be for your records only.
