Nobody needs to say how important coming out is. Whether from second or first-hand experience, everyone knows that a person coming out to someone else as gay, lesbian, or bi-sexual, is a significant life event for that person. It also means two things:
The person who is coming out to you, trusts you. They are placing something that is very personal to them in your hands. If anything, you should immidiately feel a great deal of respect for them (and if you want to be selfish about it, you could feel honoured).
It does seem a little odd, but sometimes people just want a reaction. This is not to be confused with a bad reaction; if someone sits you down to come out to you, they want a moment of conversation, followed by acceptance. If they say it in passing, however, they usually do not want to talk about it.
See, that is something you really need to remember. Everyone is different. Of course, if someone chooses to come out to you, you probably know their personality pretty well. You know that they love Doctor Who or Keeping up with the Kardashians and hate golf or dancing. This is someone you know. This is your friend, new or old, that is sharing just a bit of themselves with you.
So, what do you do?
Be compassionate. It should go without saying, but allow them to talk, and get out all of what they want to say. You may be one of the first people that they are choosing to talk to, perhaps even before their family. That means they will probably have a lot to say (again, I stress that this can be down to the person. If they’re usually guarded about their feelings, they may just want it over and done with – but still remember be compassionate).
Be selfless. I know this may seem unrelated but recently, after having a conversation with my friend who is pro-life (I didn’t know), I was reminded that it is always good to be mindful that some people do not feel and think the same way as others. So if after someone comes out to you, you personally "couldn’t understand" or "would never do it" and think "ugh, kissing someone of the same sex?!?" – even if it creeps you out, and you have the urge to say "I have nothing against it but personally...," just do not say it.
Don’t jump into accusations of "how do you know?" They’re not lactose intolerant, they did not have a bad batch of straight and now realise that some gay-almond milk is the way forward! They know. Trust that their feelings are something they understand and push aside any accusations. But even if they are unsure, sexuality is fluid (as in gender, but that’s a different topic) and it can grow and expand and change.
Don’t get me wrong, if you have questions do not be scared to ask… but make sure they’re well-thought-out.
Things to consider
It has been a while since I have experienced a ‘coming out’ situation, but there is now so much advice and support available online, so that would be a good place to start if you have any awkward questions.
In fact, something you may experience at university is someone’s second ‘coming out’. That is when they have already come out back home where they live, and now they find themselves in the awkward position of having to do so again. This is sadly something that happens a lot.