Comment by MrAnalogy

There isn't necessarily no way to communicate. It's normally just language (or symbolic) communication.

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.