A common problem in hand knits using a lot of stockinette stitch (knit each round or knit facing side and purl back stitch) is that the side selvedges and top and bottom edges curl. The nature of a knit stitch is that the back side is slightly shorter than the front facing garment side. Additionally, the bottom and top of the stitch are the anchoring pieces, experiencing greater pressure, causing the stockinette fabric to curl inwards. While a rolled hem edge can look great on children's sweaters when it is a design element, the curling of stockinette stitch can detract from most sweaters, cardigans, scarves and other knitted items.
If you want that curled, rolled edge, all you need to do is have a good four or five rows of stockinette at an edge. If you want to prevent the curled edge, follow these tips:
Use A Different Stitch There are many knit stitches that produce a nice, flat fabric. Seed Stitch and garter stitch are two of the most common. You can knit your item entirely in these stitches, or for the sides you can add a selvedge edge of at least 4 stitches in the flat stitch of your choosing. Testing this out on your gauge swatch will let you know if 4 stitches is enough, or if you need more.
For sleeve cuffs and bottom edges, ribbing is a nice stretchy, flat edging that does not curl. Bottom edges of garments usually need at least 3/4 inch in order to prevent curling. Your garment may need more for comfort and wear.
Add An Afterthought Selvedge If you have already knit your item and are hoping to fix the curl, you may be able to pick up the surrounding edges and add on a flat knit edge, at least four stitches each. You can also crochet on a decorative edge. Many crocheted edgings lie flat and will help to prevent your knit fabric from curling at the edges.
Block The Item Flat You can try to block the knitted piece to see if blocking will stop the curling. Check the manufacturers guidelines for how to block or finish with the yarn used in your project. For example, blocking most wool items means getting the item wet with cold water, carefully removing the excess water, and then smoothing the item out flat into the shape it should be and letting it dry. Some yarns can be steamed into shape. Remember to never add any combination of heat, alkalinity or agitation/rubbing to a yarn that will felt. You will have a felted knit piece instead!
Blocking the item is really a temporary solution, and it doesn't always work for curling. Each time the knitted piece gets wet or cleaned, it will need to be reshaped flat. Sometimes a flat blocked piece will curl while it is just being stored.
Overall, if you want to avoid curled edges start by making sure you have an appropriate flat edge stitch around your piece and that you have tested how this works on your swatch. This can save you a tremendous amount of ripping and reknitting.