I found the stitch pattern for this on New Stitch a Day and used it to make a nice infinity scarf for my cousin. I added a simple border (because I'm always afraid of curling edges).
-knitting needles, size 6.5 mm or US 10.5
-steel yarn needles, size 7cm (for sewing finished ends together)
-2 balls of yarn, Red Heart Boutique Midnight - 1933 Aura
-knit 2 together (k2tog)
The following pattern is the one I used and modified to make the infinity scarf:
Cast on 42 stitches
Rows 1-5: knit
Row 6: k7,*p4, k2; rep from * until last 5 stitches, k5
Row 7: k5, p2, *(k2tog but do not sl from needle, insert right hand needle between the sts just knitted tog, and knit the 1st st again; then sl both sts from needle tog) twice, p2; rep from * until last 5 stitches, k5
If this step is confusing, definitely check out the video from the New Stitch a Day link above.
Row 8: k7,*p4, k2; rep from * until last 5 stitches, k5
Row 9: k5, p2, *k1, k2tog and knit 1st st again as before; k1, p2; rep from * to last five stitches, k5
Repeat rows 6 to 9 until you have the desired length for your infinity scarf. Cast off and make sure you cut enough string to sew your two finished ends together.
The first image below shows that both sides of the infinity scarf have different, but nice patterns. One shows the broad spiral rib, and the other side shows a plainer rib pattern. I'm only mentioning this because some patterns I've worked with are nice on one side, but flip the work over and the other side is not quite so nice-looking. Fortunately, both sides turn out splendiferously for this pattern :D
Broad spirals up-close and personal:
This is the finished product:
And now, all tied up to give as a present. Yahoo!!