Certain knitting stitches are notorious for curling at the edges. Stockinette stitch -- knitting one row and purling the next -- is one of the worst offenders. Once a piece starts to curl there is not much you can do about it. The best way to keep knitting from curling is to plan ahead and add a border in a non-curling stitch to your pattern. Seed stitch is an easy one to add. It has a bumpy texture formed by alternating knit and purl stitches.
Cast on the number of stitches you need for your pattern plus eight additional stitches.
Knit one stitch, and purl one stitch across the row. If the number of stitches is odd, start the next row with a knit stitch. If the number of stitches is even, start the next row with a purl stitch. Continue alternating knit and purl stitches across the rest of the row. This is the basic seed stitch pattern which is very resistant to curling.
Repeat Step 2 for two more rows.
Knit the first four stitches of the row in seed stitch, knit the rest of the row according to the pattern and add four more seed stitches at the end of the row. Continue in this manner until you reach the last row of the pattern.
Knit four rows at the end of the pattern in seed stitch and bind off.
Adding a border in seed stitch will increase the size of your knitted piece slightly. Adjust your pattern, if necessary, accordingly. Add more rows in seed stitch for a wider border.