Summarize:

You're going to be devoting a lot of time to it when you are a staff member., so make sure you will enjoy it. Don't go right in with asking for staff. Not only is this rude, you may get banned. Gradually start telling the players and owner (if there) get to know you. Be the first to provide help to players in need and conform to the rules. Be nice, don't curse a lot (unless it's allowed on said server), and help newcomers enjoy the server. Be nice. Give people tips, post funny stuff and talk about a great part of the server.
Find a Minecraft server that you really like. Introduce yourself on the server. Make a good example of yourself.