Stockinette stitch is one of the fundamental building blocks of knitting, but beginning knitters making their first scarves are often horrified to find their neat stockinette fabric mysteriously curling up at the bottom and backward at the sides. They haven't done anything wrong. It's just the nature of stockinette to behave this way. When making a flat article from stockinette, it's wise to use non-curling border stitches to counteract this roll. Wet blocking is a temporary remedy for a completed article. Lining it is a less familiar cure, but presents creative possibilities.
Knit about eight rows of a non-curling stitch, such as the garter, moss or ribbing stitch, to create a non-curling lower border. Knit two to four garter or moss stitches at the beginning and end of each row to form a more stable selvedge.
Wet-block the knitted article to discourage edge curling, at least temporarily. Dampen the knitted piece with a spray bottle, then roll it in a towel. Press the towel to squeeze out extra water -- never wring a piece of knitting -- then unroll the towel. If you're working with natural fibers you can also dampen the project with steam from a steam iron, but don't use steam for synthetics -- the heat kills the resilience and drape of the fibers.
Lay the piece of knitting on a towel-covered blocking board -- this can be anything from a piece of corkboard to a mattress -- or, if you don't have a blocking board, use the carpet. Arrange the garment into the desired shape -- it will dry exactly like this -- then pin the edges flat and allow it to air dry.
Line your knitting with a stable woven fabric, which counteracts the stockinette stitch's tendency to roll. Whenever possible, use a fabric made of the same material as the yarn in your knitted project -- that way, you won't run into problems when it's time to launder the piece. Pre-wash the fabric before using it as lining. Velvet and satin can be used to back scarves made from alpaca or silk, which may require dry cleaning to prevent shrinking and bleeding.
Cut the lining a quarter-inch larger in all dimensions than the knitted piece it will back. Pin it to the back of the knitted item, turning the edges under a quarter-inch to hide the raw edge, then stitch in place.
The knit stitches in stockinette are taller than they are wide. Purl stitches are as tall as they are wide. The difference in their dimensions is what causes a flat-knit piece to curl toward the back on the selvages and upward at lower edges. The borders and blocking techniques here may not eliminate that curl entirely, but they will reduce it.
Although stockinette fabric always curls, the tension of tightly-knitted stitches can make that curl worse. If you have the option, opt for a looser gauge -- that is, use larger knitting needles or less tension on your stitches -- to naturally reduce the amount of stockinette curl.
If you're knitting a garment in multiple pieces, don't worry about stockinette curl along the edges of pieces that will be sewn together. Once you stitch the pieces together, the fabric will lie flat.