The most common and basic business entity is a Sole Proprietorship. It refers to a single owner with no liability protection of personal assets. If there are no employees, Sole Props can operate under the owner's social security number.  

Tax-wise, sole props are filed on a Schedule C with the individual’s personal return on the federal tax Form 1040.  Additional tax forms may be needed to report all the business' expenses.  The Sole Proprietor takes draws against earnings but pays tax on the total net profit of the business, including Self-Employment tax (Social Security and Medicare). 

Spouses who jointly run a business may both be considered owners for tax purposes.  Each would file a Schedule C and Self-Employment Tax schedule.  Income and expenses of the business would be split between the each spouse based on work interests and time spent on the business.  To choose this option, both spouses must materially participate in the business, they must be legally married and eligible to file a joint tax return.