Scrubbers, scrubbies, tawashi-- whatever you call them, they're apparently a popular crochet item. I made a bunch of them to stick in with Christmas gifts, and now I've whipped up a couple to keep. I like them because they're simple, quick projects that don't require a whole lot of attention, so I can listen to TV while I work. They don't use much yarn, so they'd be a nice way to use up scraps. Best of all, they don't require any fancy schmancy yarn; even the scratchiest, cheapest acrylic is fine for a pot scrubber. In fact, some say that the scratchier they are, the better they work!
This is the pattern I use-- one designed by "Granny Judith": Spiral Scrubbie. There's a link to a video that is particularly helpful once you get to the end of the project.
All you need to know to get started is chain stitch and single crochet. This pattern is a good introduction to crocheting in only one loop (in this case, back loop only) and increasing and decreasing. A clever construction transforms a simple parallelogram into a round scrubber with sprial ridges. Use variegated yarn to produce attractive striping-- or switch colors every two or three rows for more even, pronounced swirls.
(I think that the next time I make these, I'll use two or three colors of yarn per scrubbie and make cheerful "lollipop" designs.)
Here's a similar pattern, minus the spiral effect: How to Crochet a Tawashi.