Hi Deb, and how cool that you've started knitting! If you are knitting a row and then purling a row, you're doing stockinette stitch. It's going to curl no matter what you do...it's just the nature of that particular stitch pattern (not all knitting curls, though). Even blocking won't help

To keep the stockinette pattern, you could do the following:
When you start the scarf:
Start out knitting 3 or 4 rows (or more) of garter stitch (straight knit stitch)
Then, on each edge of your scarf, do a number of stitches in garter stitch (do the same amount on each side)...they'll make a border. When you get to the end of the scarf, do another 3-4 rows of garter stitch (just make it consistent with what you did at the beginning.) This will help to keep your scarf from curling. Remember to include those *extra* stitches on the borders in your total number of stitches for the scarf. You can use stitch markers to remind you that you're coming to the border stitches, so you won't forget to knit them when you're on a purl row (been there, done that LOL).
Just play around with it. Depending on the yarn you're using, your border (top, bottom and sides) might require more or less stitches to keep it from curling.
Also, check out the following site:
knittinghelp.com
Great videos to learn knitting. If none of this has made sense, PM me! Good luck to you!