W4s and W2s:
If you have a job where you get paid a regular salary or an hourly wage, and taxes are withheld from your paycheck, then you are considered an employee, and you will fill out a W4 form when you start work. A W4 looks like this, and it tells your employer how much tax to withhold from your paycheck.
At the end of the year, you will get a W2 from your employer. This is a summary of how much you were paid and how much tax was withheld from your paycheck. You use this information to file your income taxes. Then the government can see if you have had too much or too little tax withheld, and you will either owe taxes (bummer!) or get a refund (yay!).
If you have simple taxes, you might want to use TurboTax. If you have complicated taxes (like lots of investments or something), get an accountant. It is worth it to not have to worry about the scary men with briefcases knocking on your door in the middle of the night.
W9s and 1099s:
W9s and 1099s are for contractors. Contractors are people that do not actually work for a business, but they provide outside services. Examples include landscapers, freelance writers, accountants, lawyers, website designers, etc.
When a contractor performs services in excess of $600, they need to fill out a W9 form that looks like this and the business will issue a 1099 at the end of the year. A 1099 is a summary of the payments that the business has made to the contractor during the year.
Here is the thing to remember about contractors: the business does not withhold any taxes, so the contractor is responsible for paying all the taxes at the end of the year. If you are a contract worker, it is a good idea to set aside a chunk of your earnings so that you don't get a nasty surprise when you file your taxes.