Sometimes they don't.

My friend's grandmother had a stroke some months back; she lost the ability to talk. She can easily demonstrate that she understands what you say, but she can't talk.

There is a passage in The Language Instinct about a man who had a stroke, and lost the ability to talk. He recovered. And he described the experience -- of finding himself in difficulty, knowing something was wrong, and calling out to his wife for help... when no words came out.

It's one of the most horrifying things I can think of. :/

So, you could communicate with hand gestures, pictures, etc.

One technique is a communication board, with lots of pictures. The person with aphasia would point to the picture of concept they want to communicate.

And there are augmentative communication devices, but they are ( in my experience) not terribly useful for an adult w/ aphasia.