If RS is in stocking stitch:
- start with both yarns held at the front
- bring working yarn to the back and start working in st st
- at Beginning of Round (BoR), first bring yarn from old skein (the one you just worked with) to the front, then bring yarn from new skein to the back (no interlocking between yarns)
If RS is reverse st st, then you do the opposite:
- start with both yarns held at the back
- bring working yarn to the front and start working in purl st
- at BoR, first bring yarn from old skein to the back, then bring yarn from new skein to the front
Below is the video I learned from (the demonstration of this technique starts at minute 1:55):