First of all, make a nice resume. When you go applying for a job you will need one of these, and it makes you look organized and professional. It would be very wise to save the resume copy on your computer so that you can copy the template and update it/create a new one when you want to go look for a different job in the future. Over time as your employment history builds, your resume will start to look really great
Second, at a young age it can sometimes be hard to find "legal" work, as they usually have an age limit that you need to meet (16) and other stupid things like that. One of the best ways to get yourself into the work force is by word of mouth!
When I under 16 years old and wanted to start working, I got my parents and my friends parents asking around or keeping their eyes open for jobs. I ended up scoring a gig through my mom's friends husband, who owned a landscaping company and needed a young guy to come work as a labourer on one of his crews. This was a great first job for me, and I was able to put it on my resume and show that I had some work experience when I turned 16 and went applying for a regular job.
As for different types of jobs, alot of young kids start working at places like fast food joints, because those people avidly hire young kids. The problem with these sorts of employers sometimes is that they hire young kids INTENTIONALLY, so that they can take advantage of you. For example - McDonalds will often hire young people as soon as they turn 16, and instead of paying them the minimum wage of $10 per hour (like all jobs legally must pay), they will find a legal loophole and pay you $6-8 per hour as a "training wage", until you have amassed a certain amount of hours.. usually something ridiculously high, like 500 hours. Then they give you a measly few hours per week and VOILA, you are officially a human slave.
Try applying at something like a local market, or a grocery store. Many of these places make great first jobs, and are happy to hire kids part time
Another good option might be a job in the retail industry. This would allow you to maybe choose to work somewhere that interests you, for example, if you like clothes you could apply at a couple of your favourite clothing stores. Or even something like a movie theater, they almost always hire young people just beginning to work, and you get cool benefits like free movies!
Unfortunately, the options are not always great when you first start looking for work, but I'm sure with some motivation & a little luck on your side, you can find something that is enjoyable and that is perfect for you. Good luck, and just remember to make a nice, neat resume and make sure you look clean, presentable, and friendly if you have to go in for a job interview anywhere. If you can impress an employer at first glance, then you have a much greater chance of getting hired than if you look like a total slob who just walks in off the streets.