There aren't enough orchestras or full-time teaching gigs in the world to accommodate the deluge of new graduates that leave music schools every year.
It's not enough to get your undergraduate degree anymore.
It's not even really enough to get an advanced degree.
And it's definitely not enough to simply bill yourself as a performer and leave it at that. There are many people who try this method, and they usually find themselves in a perpetual job search. You have to be more interesting than that. You need a hook.
Are you good at teaching? Do some masterclasses at local schools or teach private lessons. Do you like to write? Start a blog or write a book. (Make it an ebook to cut down on start-up cost.) If your heart is set on making a name for yourself via performance alone, collaborate and form chamber groups. Chamber music is a great way to be an active and versatile performer while retaining creative control; you choose the repertoire and the gigs, so you get to show the audience your personal style. Having several groups will keep things interesting for you and prevent burnout on a particular piece or style of music.
Regardless of the path you choose, advertising is key! Make a website and a Facebook page for whatever you're offering the world, whether it's performance services, lessons, or your blog. Weebly, Wix, and WordPress are some good choices for building a website; they all offer free versions as well as the option to upgrade to a paid account with more features.
Google AdWords and Facebook ads are two user-friendly ad services that can help you get your name out there without spending a ton of money. I've used both of these to great effect. Even a small advertising campaign can make a big difference in your online impact.
At the end of the day, it comes down to this: while you might know that you're a special, gifted, and brilliant performer, to the general population you're just another musician on the job boards. Find your way to stand out or prepare to be lost in the crowd.