The specific details depends on what you use for your checkout. You probably have to update your confirm.php page and/or pp_confirm.php depending on which checkout options you used. If those pages have a "Store Cart Summary in Database" server behavior, then they are the ones that need the new update code.
You can probably add a column to your cart for "subscriptionDays" and save the number of days for each line item there. Then you can add a calculation for TotalDays = [subscriptionDays] * [Quantity]
Then your update could get the total value of the TotalDays and add it to the users subscription. Then the userid you could get from the session variable and the current logged in user. The expires column would have to be generated. Since if they have an existing subscription you would have to add the number of purchased days from their current subscription expiration, and if they don't or if it expired in the past you would have it add the number of days from today's date. That code would have to be hand-generated above the update and saved into a variable that could be used in the Update.
Once you have the new expiration date it would just be a matter of applying the update database server behavior to update the users profile.