Over the years I've used old student IDs, insurance cards, and the like* - my current pot scraper is an expired Duane Reade savings card. Here's how it works.
*I recommend against using your old credit cards for security reasons, though anyone who's willing to do your dishes is probably trustworthy.
Step 1: Find a Card
Step 2: Scrape Pot
Use the edge of your card to scrape the bottom and sides of the pot. Curve it a bit - this will give you an even sharper edge to really work the burned-on bits. The corners of the card are great for scraping the curve of straight-sided pots.
Knock a bunch of gunk off the pot, rinse, and repeat!
I find it helpful to leave a bit of water in the pot to facilitate scraping. For really burned-on food, cover the burned area with hot water and a bit of dish soap and let it sit for a few minutes to overnight, then scrape. Repeat as necessary until pot is clean.
Step 3: Rinse, Dry, and Put Away
Nice job. Return your card to the sink to await your next cooking disaster.