My sister received a distribution statement for funds from her 403b however did not receive a 1099. how does she report this money.

[DanaB27]

Did she check online if she can access the Form 1099-R or inquire with the plan why they didn't send Form 1099-R?

If tried everything and cannot get Form 1099-R then she will have to create a substitute Form 1099-R:

1. Click on "Search" on the top right and type “1099-R” 
2. Click on “Jump to 1099-R” 
3. Select "Change how I enter my form" on the "Let's import your tax info" screen
4. Select "Type it myself"
5. Fill out Form 1099-R
6. Continue through the questions until the "Do any of these situations apply to you?" screen select "I need to file a substitute 1099-R"

She won't be able to e-file she will have to print and mail the return. 

Please see How do I file an IRS extension (Form 4868) if needed.