We file income tax because everybody shares in the liability to pay for government services such as building/repairing roads, building and maintaining schools & libraries, funding police and fire departments, funding public parks and rec services, and many other services.
When you get a job, the company will ask you to fill out some paperwork to help determine how much tax you will owe. The form W-4 will ask you if you're married or single and if you want to claim any children as deductions. Most single people choose one (1) exemption for themselves.
Once that happens, taxes for federal, state, local and Social Security will be taken automatically out of your check and your employer will forward that money to the appropriate government accounts, so there's no need for you to worry about that.
The deadline for filing your taxes in April 15th for the proceeding calendar year January through December. Your employer will give you a form called a W-2 the next January that shows how much you made and how much taxes were taken out for the time that you worked there. You'll need this form to file your taxes.
The forms to file your taxes are the 1040 EZ and 1040A. EZ is exactly that, the easiest form to use when you don't have dependents such as a spouse or kids. You can go to IRS.gov to either download the form or use their PDF to file directly with them. There are online services available to purchase but they also require additional fees to file electronically for you. Professional tax services do the same thing, and require additional fees to use their services.
In your case, your local library should start carrying tax forms in February free of charge. Doing your own taxes at this point in your life is easy - you plunk in amounts in the boxes they tell you to and work down the page. There's simple addition and subtraction involved plus looking up your tax liability in a table/graph. Depending how much you made and how much taxes were taken out of your check will determine whether you've paid enough in to cover your tax liability or have to owe. If you paid in too much, you'll get a refund of the over payment. If not, you'll have to send in an amount to equal the amount of your fair share of taxes.
You'll do this process once for the Federal level, once for the State level and once for a local taxes if that's collected in your area. That's why you get four W-2 forms, one for each filing plus an additional one for your records. Always print out or make a copy of your tax return and keep it in a safe place.
Don't worry about making a mistake, these forms are virtually foolproof. Unless you intentionally try to de-fraud the government, you will be fine. Double and triple check your work before sending it out.
Although snail mail takes about 6-10 weeks to get a refund back, I wouldn't spend any thing extra to file electronically. If you're not sure you did something correctly, there's lots of free tax advisers either at school, library, parents, employer or other trusted adult that can help you.