Military member and my spouse started a photography business in 2020.Due to the costs she will have a net loss, what do information do I need to claim her on my taxes?

Is this one person's business ?    Or are you running this together ?   Did you apply for an EIN yet ?   What state do you live in ?  

You don't actually "claim her" on your return.  A spouse is never a dependent.  You should file a Joint return for both of you combined.  Or do you just mean to claim her business stuff?

You need to report her business.  You can claim a loss on your return.  To report self employment you will fill out schedule C in your personal 1040 tax return and pay SE self employment Tax.  You can enter Self Employment Income into Online Deluxe or Premier but if you have any expenses you will have to upgrade to the Self Employed version.  How to enter self employment income

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

For the future, you should use a program like Quicken or QuickBooks to track your income and expenses.  There is a QuickBooks Self Employment bundle you can check out which includes one Turbo Tax Online Self Employed  return....

http://quickbooks.intuit.com/self-employed

You need to report all your income even if you don't get a 1099Misc. You use your own records.  You are considered self employed and have to fill out a schedule C for business income.   You use your own name, address and ssn or business name and EIN if you have one.   You should say you use the Cash Accounting Method and all income is At Risk.   

After it asks if you received any 1099Misc it will ask if you had any income not reported on a 1099Misc. You should be keeping your own records.  Just go through the interview and answer the questions.   Then you will enter your expenses.

Self Employment tax (Scheduled SE) is automatically generated if a person has $400 or more of net profit from self-employment.  You pay 15.3% SE tax on 92.35% of your Net Profit greater than $400.  The 15.3% self employed SE Tax is to pay both the employer part and employee part of Social Security and Medicare.  So you get social security credit for it when you retire.  

Here is some IRS reading material……

IRS information on Self Employment

http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Self-Employed-Individuals-Tax-Center

Pulication 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