The odds of your making a living performing your own material are small, vanishingly small. But there are a lot of ways to make a living in music. If you do succeed at the singer-songwriter path using the tips listed in the other answers, mazel tov. In the likelihood that the singer-songwriter-musicia
I have one friend who’s a full-time professional singer-songwriter, touring on the lesbian folk circuit. She puts out albums once in a while but those aren’t a major source of revenue; they seem mostly to serve as souvenirs from her gigs. She supplements her touring income with some freelance non-musical work around the sides. Her life is possible because a) she’s just unbelievably good at what she does, b) she’s well-connected to a warm circle of fellow singer-songwriters who form a mutually supportive scene, and c) she doesn’t mind living on the road for long spans of time. I did a little light touring with a band that she was also in, and it just killed me. I couldn’t take it, even for a few days at a time. I need to be close to home. So no touring musician life for me.
Another singer-songwriter of my acquaintance also tours constantly, though not in support of her own work. She’s a horn player who does gigs with a few very high-profile pop acts, several medium-level bands in wildly different styles and many local and session gigs around the sides. Her own material doesn’t seem to be much of a source of income, though that may change someday. She can make her career work because she’s a highly versatile and well-trained musician adaptable to any situation. Also, she has a master’s, so she can get good teaching jobs. She’s also easy to get along with, and has a high tolerance for life on the road. There are times when I envy her, but I get upset when I have to play music I don’t like, and she has a high enough level of professionalism to be able to enjoy whatever she’s playing, so she’s better suited to her life than I would be.
A trumpet player and singer I know has been fronting a series of bands for several years. His current one substantially supports themselves through busking, along with occasional tours, private parties and the like. For several years he mostly paid the bills as a web programmer, and also led percussion classes for corporate groups on company retreats, but has mostly stopped needing to do that. Busking is hard work that doesn’t pay well, so his life is a little on the ascetic side — I admire his commitment tremendously.
A bassist I’ve done a lot of work with has been working cruise ships for the past few years. On the plus side, he gets paid to see the world and play his bass every day. On the minus side, he’s even more nomadic than people who tour, and he has no say about the music that he’s playing. I understand why he likes it but you couldn’t pay me enough.
Other singer-songwriters I know who perform and record at a pro level have day jobs ranging from music therapy to commercial illustration to beer distribution to cartoon voice acting to various kinds of teaching. Some folks also do weddings and DJ gigs, production, film scoring, commercial jingles, musical theater or children’s music. I know very few musicians who have no other kind of job at all; most of them are either independently wealthy, or have very supportive significant others, or simply choose to live in abject poverty.
As for myself, I’ve found that it’s more important to me to play music that I like and that I have artistic control over than it is to be involved in music in any capacity. So I work full-time at the ACLU doing online outreach, a job which I like very much. I produce tracks at night and on the weekend. I gigged really heavily for a number of years but have pretty much completely stopped, because the low pay and general indignity of the live music world isn’t worth it to me anymore. I love teaching lessons and hope to do that forever. I also record and produce other people’s stuff, which sometimes I enjoy, and which sometimes is just as tedious as any other kind of technical work. I love film scoring and theater, and would like to be doing more of it, but in the meantime am content to pursue my own ideas and whims and give away the results on the web: http://soundcloud.com/eth
I guess my point in saying all of this is that there are many different ways to be a musician, and the word “professional” encompasses many different ways of making a living. It’s up to you to figure out what you enjoy, what you can get paid for, and how to juggle it all with the other demands on you as a person. Good luck!