Hi,
At 13 the transition will be a lot harder then if you wait till you are say in your late teens, however it can be done of course. The challenge will be deciding what type of market you want to perform in, if you are looking to get into the corporate market it will be hard as companies are looking for people that are more mature and experienced in most cases( not all). One way that would be perfect for your age would be to start by doing birthday parties and build your name locally that way. By doing this when you are older you will already have a reputation and some experience and then doing the more mature and adult shows will be easer to sell.
To get started I would suggest to anyone even people that are older and full time performers study marketing and courses on business. There is a lot more to this then just charging money, you need to learn how to run a business, keep customer retention up, and how to market to your target demographics. Dave Dee has an excellent course in marketing for magicians that would be a great way to get you started and learning how to do this.
So you know, I do this full time and when I am not doing shows I am marketing and doing the business side of things. It is a full time job for me, I spend on average 30 plus hours a week doing the business side and probably on average only do about 10 to 12 shows a month.
With that said, start small and don't bite off more then you can chew. Its very rewarding, but also a lot of work. When I first started doing magic I didn't do a paid show till I was much older in fact I didn't do my first paid show till I was 19 and I started when I was 12.
Also study acting, lighting, sound and anything regarding stage work, this will help you become a better entertainer and teach you how to handle anything that can happen when you are performing.
Hope this is enough to get you started and of course if you have any questions feel free to contact me.
Besides all the great advice Todd has given you, I would just add...be active in promoting yourself as a working Magician. By that I mean, have some Business Cards or Flyers printed up...advertising yourself as a Magician for Hire.
Publicity is always good, as well. Perhaps do a few Volunteer shows at local Hospitals, Care Facilities or Non Profit Organizations...Alerting your local News Media about your performances. Getting stories published in your local Newspaper or Television coverage by your local News Station can assist you in getting your name out there.
These guys have given you some great advice. I think I would advise you to practice for 2 more years, at least. Then when you have a repertoire of effects from which to choose, put together a routine/act of about 10 or 12 tricks.
Only then would I (if at your level of skill) begin to peform for birthdays, etc.
You'll also find, in time, that it takes about 20 years, or so, to really find your niche, and to develop your character, (Once you do start performing).
You've got a lot of work ahead of you. So, keep rehearsing, and start thinking about the type of act you want to do. Close-up or Stage. Silent or with Patter.
A one man show or an audience participation act. With music or Without., Etc.
You have gotten a lot of good advice from some seasoned professionals. I would like to add a bit more.
Samuel Patrick Smith, the editor of the Linking Ring, also has a lot of material concerning promoting yourself. In an article he wrote for MUM, he described and incident that showed him something he had left out of his material.
Samuel did a lot of school shows. These can be very lucrative, if you have the right material and you know how to promote yourself. It's not Las Vegas, but it's steady income. He approached a school principal he had worked for in the past, and the fellow told him that the school had decided not to use magicians for their school assemblies. He asked the principal why. The answer surprised him.
In the year that Samuel did not perform for this school, another magician offered to do the job at a lower price. He wasn't very good. So this bad magician killed that particular venue. Samuel asked him the name of the magician, and it was one of the fellows who had purchased the promotional course from him. The complaint the principal had was that the man didn't seem to have an act.
Then Samuel realized that nowhere, in any of his promotional material, did he tell the prospective performer that he needed to have an act. He thought that was obvious and a "given." Well, it isn't obvious. There are a lot of performers who go out onstage, do a handful of unrelated tricks and think it's an act. It's not.
So before you do anything else, get some help from somebody in your area who knows something about constructing an act. This could be an older magician, a retired professional, or just someone whose work you respect.
Work on your performing character, that is, your persona. When you figure out the kind of act that will fit your natural personality and physical demeanor, then construct your act.
I'm a fat guy. I would look ridiculous doing The Dancing Cane. But I can be very mysterious. I could easily do The Dancing Handkerchief.
Plan to try a lot of things before you find the ones that are "golden" for you.
You need to study business. You need to study dance. You need to study acting. A creative writing course would help.
I have started a group called "The Business Side of Magic". It is a series of lessons that take you from a beginner all the way to a professional. Or you can just jump in anywhere that fits you. It's focused on the non magical - business side of the industry. It's not that glamorous but it is necessary if you want to advance your hobby into a profession.
Come join the group, read the lessons, ask your questions, and share your insights.