So, I just became an “independent contractor” – so now I’m going to have to keep track of how much I earn and all that fun stuff. I’m willing to do it. That’s cool. But now one of my fellow independent contractors was telling me all this stuff he was going to be able to write off. Computers, office supplies, this that and the other thing. Some of the work we’ll be doing is at home on our own computers. So, I have a few basic questions: I’ve always heard the phrase “write off”, but never really fully understood it. Can someone explain it as if explaining it to a four year old? Since math isn’t my strong point. Also, what are some things I can write off that I might not think of at the time? I have an accountant who will probably do all of this for me, but I’d like to actually know what it all means.
one more question on top of that, is there anything I should know now that I’m an independent contractor? 
Write-off is referring to the costs of doing business. Now that you are an independent businessman (woman?), you will be able to deduct what it costs you to do business from the money you make. This allows you to only pay taxes on your actual profit.
The IRS has very strict rules on this though. Really, your best source for this info is your accountant. The particulars of your situation probably vary from anyone else’s, and your accountant will best know the details of what you can do.
I will say, when you set the money aside for taxes, do not forget the employer’s share of SS/Medicare! You now have to pay both parts.
I’ll second advising you to talk to a CPA.
It won’t hurt to get a program like Quick Books.
And you’ll probably need to start making quarterly estimated income tax and self-employment tax payments.
Lots of things depend on how your business is registered. Are you a sole proprietor, partnership, S-Corp, C-Corp, or something else? The IRS and the legal system look differently at each of these entities.
In general, you will be able to “write off” any expenses you incur in the process of doing your business. You can also have capital assets you depreciate. There are three basic types of tax write-offs, they are exemptions, credits, and deductions. I supplied the numbers to my accountant, he figured out where they fit into the tax system.
You will be allowed to take much larger IRA deductions. But you will also have to pay all of the taxes an employer pays.