1. Don't look like all you want is rank to brag to your friends about.
Wait for the admin to judge you a responsible person that can manage running a server. Anytime I see someone asking for rank like that, the first thing I think is "griefer trying to get WorldEdit commands," and I'm sure that thought is running through your admin's head. Be patient. Admin is not a rank given lightly on any server.
There’s no such thing as “easily” becoming an admin on a server that’s not your own. Like others have said before me, play constantly, maybe 1-2 hours a day, contribute to the community, act professionally, and help others out as much as you can. If the server has a “looking for staff” topic, try applying to that. If they don’t, wait for them to ask you. If you can’t wait that long, it’s possible to hint at it a little bit (like saying, “I’d really appreciate it if I were made staff so I could fix these sort of problems”), but don’t do it too much as it might get really annoying.
Another side note: if any server offers you an “easy way” to get Admin, let’s just say that you probably shouldn’t be playing on that server :/
As an admin of three years on a server, I can promise you that asking for a rank is the single quickest way to get moved to the bottom of the list. I don't care how nice you are, how good of a builder you are, or how political you are with other members- if you're annoying, you get bumped to the bottom.
Another thing is this- don't post topics on the official forums to help you with your little server issue. The only way to EARN a staff rank is to play often and EARN their trust.
On a side note: that server I've been an admin on for so long has never received any of my money. If they say "you have to donate to get a rank" it's not a good place to play to begin with. They will take your money and ban you.