Directions for the Lighter Circular Beginning can be found here (scroll down).

All slipped sts are slipped purlwise unless otherwise directed.

M1R
Insert the right needle from front to back under the horizontal strand which lies between the last stitch worked and the next stitch. Place the loop onto the left needle and knit into the front of the loop.

M1L
Insert the left needle from front to back under the horizontal strand which lies between the last stitch worked and the next stitch. Knit into the back of the loop.

Working wraps together with wrapped sts:
When knitting:
Slip the wrapped stitch onto the right needle. Use the left needle tip to pick up the wrap, then slip the wrapped stitch back to the left needle. Knit the wrap together with the stitch.

When purling:
Slip the right needle tip under the back of the loop wrapped around the next stitch and place it onto the left needle. Purl the wrap together with the stitch.

1x1 Twisted Rib (Worked over an even number of sts):
Round 1: [P1, k1 tbl] around.
Repeat this round for 1x1 Twisted Rib.

Wrap & Turn [W&T] – used when working short rows
To wrap and turn on a RS row, knit to point specified in pattern, bring yarn to front of work between needles, slip next stitch to right-hand needle, bring yarn around this stitch to back of work, slip stitch back to left-hand needle, turn work to begin purling back in the other direction.

To wrap and turn on a WS row, purl to point specified in pattern, bring yarn to back of work between needles, slip next stitch to right-hand needle, bring yarn around this stitch to front of work, slip stitch back to left-hand needle, turn work to begin knitting back in the other direction.

Elastic Bind Off:
K first st and pull right needle to elongate st slightly. *Insert left needle into back of st on right needle, insert right needle knitwise into next st on left needle and draw it through st on right needle, k this st and allow both sts (elongated st and st just knit) to drop from left needle. Pull right needle to elongate st slightly.
Repeat from * until all sts have been bound off.

Note about turning the heel:
Sometimes the stitches along the sides of the heel turning can be a bit loose. You can tighten these up while working the last 2 rows before working the heel flap.
After the first of these 2 rows is completed, using another needled, start at the other end of the heel needle and pull the loops one at a time to tighten them, moving the excess yarn to the end of the heel needle.
After the next row is completed, tighten the stitches in the same way, beginning at the center of the needle and working outwards.

Notes on working with two circular needles or Magic Loop method:
As written, these socks are worked using double-point needles. If desired, they may be worked using two circular needles, or one long circular using the Magic Loop method. My sample socks were knit at the same time using the Magic Loop method.
Place stitches from Needles 1 and 2 onto one circular needle or the first side of the loop, and stitches from Needles 3 and 4 onto the second circular needle or the second side of the loop.
To work the heel, leave all stitches on the second circular needle or second loop side, and work the heel as written.
To work the leg, rearrange stitches so that the stitches from the new Needles 1 and 2 are on one circular needle or side of the loop, and stitches from Needles 3 and 4 are on the second circular needle or side of the loop.

You can find out more about him and his fiber habit online here and here.