Thank you for your question, and thanks for using JustAnswer.com. You would not need a business license to do this type of work, so no worries there. However, let's take a few moments to speak about your taxes.
You can deduct any expense that is ordinary and required in order to generate income.
This means you can deduct the cost of your computer (through depreciation), and the cost of your home office
You can deduct any subscriptions you have to databases you need for your writing
you can deduct the cost of your home office
YOu can deduct any miles you may drive as a result of this work,
Here is a list of common tax deductions for freelance writers: http://freelancewrite.about.com/od/taxes/a/Common-Expenses-Of-Freelance-Writers.htm
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How would I factor in depreciation when it comes to the cost of my computer?
Well, when you use tax software you will enter in your purchase amount, and tell it when you purchased it an the software will compute it for you
Ah okay. Makes sense.