try to not to treat them as an alien. Just be a friend. Don't overthink it. Be yourself.
It's not your job to get them better, only to be a friend. If you want to go out and about with them - invite them, but don't make anything your "mission" as it were.
There are professionals for that, too many friendships burn out when people take on more than they can manage themselves and then the hurt is worse to the person with MH when they suffer the rejection of being dropped because someone couldn't handle them having burned out.
I would always ask how any of my friends are, and expect any of them to ask me in return (I have MH, so do some of them but not all) so don't never ask but there's no need to ask several times in one visit/phone call if you already have an answer. That's probably all the person wants to give out to you at the time. On the other hand if someone tells you they think the government is spying on them or they are about to jump off a bridge or something else bizarre/odd/worrying then don't freak out and never speak to them again (it's happened to me!) but say you are worried and would like them to see the dr, even offer to go with them. If they actually are on a bridge - dial 999 after finding out which one, obviously.
I appreciate when a friend is truly there for me and would probably count that as allowing me to "be elastic", not taking it personally when I'm not talkative/sociable/withdrawn but accepting me at the times I am able to chat/socialise more so without demanding I apologise for not being in touch etc.
There are a huge host of differing mental health illnesses all with different symptoms just as there are with physical health issues and unless your friend wants to confide any of their symptoms, I'd just forget the MH part of your friend. When we are well - we're just like anyone else. When we are unwell, it can be scary (for us and for you) but the kindest thing you can do is to keep your own boundaries, don't take on more than you can handle, and just say (if you are) "I'm here for you if you need me, want me to come over and bring food?" I have a friend that when I said I wasn't even up to seeing anyone even to eat food with, ordered me a pizza delivered (that in my experience has probably been the sweetest thing a friend has ever done for me during my illness'.
That's my perspective anyway as a sufferer.