Rule #1 of being a mentor is do whatever you want. It's just a symbol showing that you fulfilled some requirements and you likely at least have more than a rudimentary knowledge of the general game. You aren't expected to be anything more or less than that.

There's not really much more than that, but I can give you advice. Just don't make a big deal of it. You aren't a big shot just because of the crown, and you shouldn't act like you're special. Most players like to tackle the game without too much outside input, letting the game present itself to them as they go along. Let people make mistakes. Let people screw up. Don't make a big deal out of it. Let people learn on their own, and if it seems to you that a player might not learn on their own, or may appreciate your advice, then that's when I would suggest providing your input.

I can't tell you how many healers I've had that didn't do any damage for the entire dungeon, and guess what I did about it? Nothing. When I was a fresh healer in 2.0 I barely did any damage either. Unless it's a problem, which it usually isn't, then I'm content with the result even though it takes more time. Especially with the introduction of level and story skips, more players than ever are doing higher end content without having a proper understanding of what it is they should be doing, but the best way for them to learn is from experience, and not someone bickering at them. At the very least, whatever you do, try to be as nice as you can about it. It's just more advice, but I think it'll get you farther with much less stress otherwise.

I keep the mentor crown on basically at all times. On Gilgamesh there haven't been many new players for a long time, so I haven't had much to utilize it with outside of instances, but it's always there to let people know that I may have answers to any questions they may have. It's not something you have to actively use, and I really wouldn't suggest thinking of it in that way.

Rule #2, pretend the Novice Network doesn't exist. It's hot garbage. Stay far the hell away from it regardless of what server you're on.