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You have several options for establishing a company with another person. Here is a summary of your options:
1. Joint Venture/Sole proprietorship - Usually no formal agreement, business income and expenses are reported on each of your form 1040/Schedule C according to your percent ownership of the venture.
2. C-Corporation - Report income and expenses on form 1120. The corporation pays its own tax and owners are taxed on income they take out (dividends). Pros are legal protection, good if you plan to grow and company and sell it, Cons are double tax to small business owners
3. S-Corporation - Report income and expenses on form 1120S. Similar to a C-Corp but instead of paying its own tax, taxable income flows to each shareholders form 1040.
4. Partnership - Reports on form 1065. Income flows to partners for tax. Allows for special allocations of income if you and your friend need more flexibility on how to split taxable income
5. LLC - Limited liability company provide legal protection so you won't lose more than you have invested in the company. You can "check the box" as to how you want to be treated for tax purposes. (Usually 1120-S or 1065)
This is a quick summary. For more detail see http://www.irs.gov/businesses/small/article/0,,id=98359,00.html
For most of the businesses, you will need to apply for a federal tax id number (available on the IRS website). An S-Corp has a separate application. You will need an attorney to prepare a LLC because every state is a little different.
As far as the 1099 issue - it depends on the entity you choose. 1099s are for businesses to report services provided. If you go the C-Corp or S-Corp route, you will probably need to pay wages for these services provided, so you will need to do payroll taxes and file forms W-2 vs. 1099. If you go the partnership/LLC route, you can just take the services as member draws instead of 1099s.
Also, you will need to file your business in your state of Washington. There is usually a registration form to record the corporate stock or LLC, and annual reports to file.
I know this is a lot of information. Please let me know if you have additional questions or click to accept this answer.