I used Liidia’s Cast On from Nancy Bush’s Folk Knitting in Estonia. This seemed the most straightforward to me and has a nice tidy appearance. However, there are a plethora of braided cast ons and you are welcome to work whichever you choose.
Make a slip knot using both yarns. This will not count as a stitch but rather anchors your yarn. Keep the tails short as you’ll just be weaving them in.
Hold the yarn as if for a long tail cast on, with the CC initially held over your index finger and the MC around your thumb. Shift the MC yarn so that the strand leading back to the ball goes around the inside edge of your thumb; the strand around the outside edge of your thumb should lead to your needle.
Go under that MC strand and snag the CC onto your right hand needle: you’ve cast on one stitch. Notice that the stitch is in the CC.
Swap the position of the CC & the MC by bringing the strand of the CC over the MC.
Hold the CC around your thumb as before with the MC. Repeat the above directions: go under the CC strand, snag the MC, another stitch casted on – this time in the MC.
Swap yarn position, again bringing the yarn from around your index finger OVER the thumb yarn.
Continue until you’ve cast on the required number of stitches. (Your strands of yarn will be very twisted together – go ahead & untwist them at this time.)
You should end up with the first and last stitches the same color. You can join in the round either by passing the last cast on stitch over the first (carefully removing the slip knot) or by slipping the first stitch, working the first round, and working the formerly first stitch together with the last stitch (dropping the slip knot right before doing so – just slip the last stitch to the right hand needle, drop the slip knot, slip the unworked stitch back to the left needle, and work those 2 same color stitches together.
For further reference, see Folk Knitting in Estonia, Nancy Bush, pp42-44.