Hi,
I am making a poncho and I am on 10.5 needles on a 16 inch fixed cable, I am running out of room. The pattern states I can move up to a 24 inch cable. How do I do that? Do I just begin knitting with the new needle?
Thanks!!! 
Yes that’s exactly what you do.
It’s very common to switch needle sizes (diameter or length). On all the baby sweaters I’ve made the cuffs are knitted with a needle size one size smaller than used for the rest of the body, so when I’m ready to switch I just grab the new needle in my right hand and start knitting onto the new size.