Give the speaker regular feedback.

Showing feelings for what the speaker is saying will reassure the speaker you are listening. If something bad happened, saying something like "oh that must be hard for you" would reassure the speaker that you are listening to them. If you don't understand something, remember to get clarification when the timing is right but do not interrupt. 
I myself, have a very bad habit of not listening which is why I chose to write about Building Powerful Listening Skills.