Getting one diabolo going on top of a loop string: This is pretty much the same technique as one diabolo with sticks. Just hold the string with one or two fingers on each hand so it's like one piece of string and just go for it. There isn't much to explain!
Getting one diabolo going inside a loop string: One diabolo inside a loop moves a bit like 'around both arms' with sticks. The diabolo travels around both hands in a big circle. The string is always pulled tight by the movement of the diabolo. Both hands move in a clockwise circle, making sure that the string always stays tight, and that the diabolo stays straight. The diabolo gets spin as it rolls down the right hand side, in the same sort of way that two diabolos works. Start by giving the diabolo a little roll to your left, then let it move around both hands.
Correcting: Correction on a loop string is quite different to sticks. You have full control, but it may not feel like that to start with! I use these three correction methods: