Async and await: multiple await expressions

I understand that when an async method hits an await expression, the method returns immediately and at some point in the future the await expression returns and the method continues to execute.

Yes, if the awaitable hasn't already completed.

When execution hits the second await expression, since the method has already returned after the first await expression was hit, what happens to execution around the second await expression?

It returns control to whatever executed the continuation, which will depend on the context. In a WinForms app in the UI thread, it would just be the event loop. In a thread pool thread, it would just be the thread pool scheduler.

Chances are whatever calls the continuation really doesn't care about it at all - it's just "something to execute in a context". It's likely to go ahead and just execute whatever it needs to do next (or wait until there's more work).

The important point is that by now the first caller has the appropriate Task or Task<T> so that they can tell when the whole async method has completed.