See the photo tutorial below:
For the purposes of this demonstration, let's assume your main color (MC) is white and your contrast color (CC) is green. You are working a bunch of double crochets (DC) along in your MC, but you want to change over to the CC in your next stitch.
Start the DC as normal with the MC. Yo and pull a loop through in MC:
Yo and pull over two loops in MC:
Now change over to the CC. Yo in CC:
Pull over two loops:
Continue working DCs in the CC.