That's correct, you just knit onto the new needles.
When you are ready to change needle sizes, slide the stitches onto the needle as you normally would, but work them with the new needle. When you finish that first needle, make sure to pull the new needle through so the lengthy side is dangling from the end you just worked, and that is the end you use to knit the next needle.
Hope this helps! (and makes sense, sort of hard to describe. I think the important thing here, though, is the pulling the new needle through and using the same end to knit with really, otherwise you wind up with wrong-facing needles.)