It's fairly simple for a typical fresh adult.
At the bare minimum.........Sometime around January-April (usually Jan or Feb), your employer will send you a W2 (looks like this except you'll get multiple copies: http://www.myfreetaxes.com/wp-content/uploads/2011/11/W21.jpg) which shows your wages and tax withheld. Each employer will send you one if you work at more than 1 place. Taxes are due April 15.
To do it yourself, you can use free tax filing software from the IRS if you make <$60,000 or you can manually fill out the forms...but I'd only do this if you're really trying to pinch pennies. Don't forget to submit your state tax forms as well.
Option 2 is Turbo Tax or something similar. It will hold your hand through the whole process as well as ask you questions about your situation which may qualify you for tax credits (more $ for you). Unless you're aware of the tax credits out there, you'll most likely miss out on these if you try to do your taxes yourself. At the end it'll do all the paperwork and filing for you (federal and state...though I think state costs extra). This is what I use. I can't remember the pricing...I want to say it starts at $25, but goes up if you want them to file state taxes for you or if your tax situation gets more complicated.
Option 3 is to go to a place like H&R Block or Jackson Hewitt and work with someone who will take care of everything for you. A simple W-2 shouldn't cost much more than $50 I imagine.
If your tax situation is realllllly complicated (you generally just know it is once you get to this point), you look up a CPA or EA and have them take care of things.
