To begin this cast on you first need to make a slip knot, the tail isn't important for this cast on and just needs to be long enough to weave in later.
Using a circular needle, hold the two needle tips together pointing to the left.
Place the slip knot on the top needle.
Wrap the working yarn around both needles, bringing it under both needles towards yourself, then over both needles away from yourself. You'll need to wrap the yarn around your needles half as many times as the total stitches needed (if you need ten stitches you'll do five wraps). Finish these wraps by bringing the yarn under both needles towards yourself again and holding it in place.
Bringing the needle tips upwards, rotate your needles so that they're pointing to the right with the working yarn held above them. Be careful not to let go of the working yarn as it's not yet secure.
Pull the bottom needle to the right, so that those stitches now sit on the cable and you can use this needle to knit across the stitches on the top needle.
After knitting across the stitches on the top needle, slide the stitches on the cable back onto the empty needle, so that the two needle tips are together again. Rotate your needles so that they're pointing to the right again. The working yarn should be coming from the first stitch on the bottom needle.
Pull the bottom needle to the right, so that you can use this needle to knit across the stitches on the top needle. The first stitch on the top needle will be your slip knot, instead of knitting this, slide it off your needle and ignore it. Knit across the stitches remaining on the top needle.
Slide the stitches on the cable back onto the empty needle, so that the two needle tips are together again. To complete the Turkish cast on you need to knit the stitches on both needles once more.