The pass is available for purchase directly at a number of locations, as per this list.
You can not collect receipts and turn them into a pass after the fact (given that receipts rarely list any person details, if you could do this you'd expect to see people selling receipts for below face value on eBay!).
You can upgrade a single entry receipt into a full pass by paying the difference within 7 days, with a few conditions - the details on this are below.
Keep in mind that the 'America The Beautiful' pass is only valid at Federally managed areas, and does not gain you entry into any state managed parks/etc. With park entry to National Parks ranging between free and ~$25, you'll need to visit a reasonable number of parks to make the pass worthwhile.
From the FAQ for the pass :
12. If I visited a Federal recreation site and paid the entrance or use
fee and I have the receipt, can I trade in the receipt and pay the
difference to upgrade to an Annual Pass?
Generally, no. When you are making your purchase, you should carefully
consider which one of the fee and pass options best suits your needs.
National Parks will ONLY upgrade entrance or use receipts from
National Parks to an Annual Pass, and will NOT UPGRADE entrance or use
receipts from other land management agencies. Any upgrades must be
done IN PERSON AT A NATIONAL PARK, within 7 days of the original entry
receipt purchase date.
Currently, the other four land management agencies (USDA FS, BLM, FWS,
Reclamation) do not upgrade day-use entrance receipts to Annual