When someone comes out to you, find out if they are out to everyone, to just you, or maybe only to a small group. It's your responsibility to maintain confidentiality and not to suggest that they come out to more people. Then ask the most basic question of all: Is there anything I can do? Typically, they may be looking for someone to be with them when they come out to other people (like at work or to family), or they just may need to hear that someone supports them.
From there, your role is to keep learning. This prepares you to be an active ally—which is going to be important to your friend. Learn how to respond when someone says or does something that isn't inclusive. Initiate conversations about LGBTQ issues in your everyday interactions. It's also nice to have something visible to signal your support (a rainbow flag or ally pin) when you can.
And remember that being an ally means including the entire LGBTQ community. This will signal to your friend that your support is truly sincere.