If your career is going to be in modeling, then you need to look at it as a business. Just as if you were starting your own business, you'll need to put in time, money, and effort to make it work.
The time needed to start up the business of marketing yourself is hard to gauge. Luck can come into play. You could be discovered walking in the mall with your friends while shopping. Then again, like most models, you might have to go to one "meet and greet" after another before you find a client who wants to work with you.
The money comes in to play by paying a photographer to take some good photographs of you. This is of course after you sign with an agency. Before then, all you need is a couple of Polaroids to sell yourself to the agency and get them interested in working with you. You'll need much more professional-looking pictures to get clients interested in doing business with you.
Effort plays an important part in how quickly you find representation and your first paying gig. Join up with an online site like Explore Talent .com to get an online presence so talent agents and clients can find you.
If you are lucky enough to get an agent simply by sending in some photos of yourself, half the battle is over. Of course, this doesn't mean you should park your butt in front of the TV and let your agent do all the work now. Get out of the house and start networking with people in the business. Go to fashion shows, hang out at modeling hot spots; in short, put yourself out there to get noticed by agents, clients, and photographers.
Following through in all three of these areas will up the chances of your success exponentially.