Why am I not getting federal taxes taken out of my paycheck?

Contact your employer.

Did you complete a W-4 and give it your employer?  Use this IRS website for a tax withholding estimator - https://www.irs.gov/individuals/tax-withholding-estimator

The W-4 you filled in and handed to the employer will determine how much if any taxes are withheld based on the gross paycheck.   The new W-4 form put in place a couple of years ago tries to get the bottom line of the return to zero.  If you want more withheld then you need to adjust the W-4 form ... start by choosing the SINGLE/MFS box if you have not yet done so.  AND/OR reduce the number of kids in step 3.   AND/OR  add an amount to line 4C of your choosing.   

You can also use the worksheets for the W-4  if you wish : 

https://www.irs.gov/pub/irs-pdf/fw4.pdf

Or.....are you being paid as an independent contractor?   Are they taking out Social Security and Medicare?   If nothing is being deducted, better ask if they are going to be issuing a 1099NEC to you instead of a W-2.   If you are being paid as an independent contractor you are going to have to file as "self-employed" and pay self-employment tax and maybe ordinary income tax at tax time.