Yes, you need to declare that income, but you don't need to open a business to do so. You can report the income as "Other Employment Income". 

If I make $1000/month, do I need to open my own business? 

As you make less than $30 000 a year, you do not have to claim as a business. 

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If I make more than $30000 by doing administrative support (printing, filing, faxing, using computer) and also filing taxes and accounting support, what kind of business should I open? Can I be self-employed?

Yes you would be self-employed:

1. If you provide a product or service with the intention of making a profit you are considered self-employed.
2. You can deduct your self-employed business expenses on your tax return as long as they helped you generate income.

The Beginner’s Guide to Self-Employed Taxes

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