The first confusing thing you have to conquer when knitting two socks at a time of two circular needles is the fact that you don't knit all of sock one and then all of sock two. Instead, you knit the first half of sock one, then the first half of sock two (these stitches are on the same needle). Then you knit the second half of sock two and the second half of sock one from the other needle.
So, to get started, situate the needles so that you can knit the stitches from the first half of the first sock you cast on. Remember you are always keeping the stitches on the same needle they started on, so if your needles don't match, you're always knitting stitches onto the needle that looks the same as the needle you're knitting from.
For the purposes of this sample sock tutorial, I just knit across all stitches, but if this were an actual sock, you'd probably work ribbing here.