A web search for "exploit chain uaf" found me a few real-world and a few tutorial examples, though I don't know which are good.

At a high level, though: once you've gotten a new object allocated where the old one was, you now have two different views of the same bit of memory. You use valid operations on one view to put the other one into a corrupted state. For example: in a unixlike kernel, maybe one view has a field containing a function pointer (for method dispatch, essentially). You read that field using the other view, use it to deduce something about the target's memory layout, write a new value to the pointer, then use the field via the first view to cause execution to jump to a location you control.