How do I report a business with no income? (I would like to deduct my losses and file a return) I have options for a variety of 1099 forms, but none of them apply yet.

Use the GENERAL option for any income not on a 1099 .... but if you have a working business that has had no income simply skip the income section.  But if the business has not yet "opened it's doors" then you cannot take the start up expenses yet.

If you are new to being self employed, are not incorporated or in a partnership  and  are acting as your own bookkeeper and tax preparer you need to get educated ....  

If you have net self employment income of $400 or more you have to file a schedule C in your personal 1040 return for self employment business income. You may get a 1099-NEC for some of your income but you need to report all your income.  So you need to keep your own good records. Here is some reading material……

IRS information on Self Employment….
http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Self-Employed-Individuals-Tax-Center 

Publication 334, Tax Guide for Small Business
http://www.irs.gov/pub/irs-pdf/p334.pdf 

Publication 535 Business Expenses
http://www.irs.gov/pub/irs-pdf/p535.pdf 

Home Office Expenses … Business Use of the Home

https://www.irs.gov/businesses/small-businesses-self-employed/home-office-deduction

https://www.irs.gov/pub/irs-pdf/p587.pdf

Publication 463 Travel, Gift, and Car Expenses

https://www.irs.gov/pub/irs-pdf/p463.pdf 

Publication 946 … Depreciation

https://www.irs.gov/pub/irs-pdf/p946.pdf