In addition to the above responses, some IRC networks (usually the tiny ones with few active users) have an application form on their website for those wanting to be an oper, something that I find strange given that I support the appointment method described here by some of the other contributors. Access to the IRCd is not something that I'd give, if I was in the position, to people that I don't know and therefore can't trust. That is not meant to be a slur on people who show an interest in being an oper, but instead an understanding that not everyone who shows an interest has a networks' best interests in mind.
If you deserve a chance then it may come one day. Patience is a required pre-requisite for many reasons. If you are in a hurry for access then you'll most likely be in a hurry regarding most or all aspects of being an oper and that is not always a good thing.
One last thing to remember is that any percetion of power and glory is a myth, not a legend. I've been an oper for a while and I can say that at times I spend time finding ways of avoiding the job as much as doing it. It's not what it's cracked up to be sometimes.