My mom knits dish cloths. She uses only cotton yarn. You could just crochet a square, then crochet around the edges.
There's also a TV show on PBS. I think it was called Knit or Crochet Now. They make a square with a new pattern in every show. Many of those would be suitable for dish cloths.
Search Lion Brand Yarn and Red Heart Yarn. They have sites with tons of free patterns for crochet and knitting. I love to crochet. Keeps my hands busy and gives me a break when my sewing gives me a fit.
There are lots of crochet patterns free online just google free crochet dishcloth patterns and knitting ones to if you knit. Libby