How do I keep a scarf from curling after and while I knit it.?

Some knitting stitches pretty much always curl and there is nothing you can do about it. Stockinette or any stitch pattern where you mostly knit one side and mostly purl the other side is probably going to curl.

You can try blocking the scarf after you knit it to help it lay flatter - wet it and pin it flat. Blocking works best with natural fibers, but I've had some mild success with synthetics like fur and ribbon yarns.

The best way to avoid curling is to use a stitch pattern that doesn't curl. Examples: garter stitch, ribbing, moss stitch, double moss stitch. I'm pretty sure most reversible (front and back look the same), stitches won't curl.

Good luck!

Do you knit stockinette scarves? If so, that would explain the curling. Try to incorporate a moss stitch (alternate knit and purl) border into your scarf design. Or do a few rows of ribbing at the ends of your scarf.

I know that ribbing will keep a scarf from curling. It looks like that may be the only way:

http://experts.about.com/q/2228/3921584.htm

it is not the project that curls it is the yarn as it comes of theball