If my employer has not withheld social security and medicare taxes, how do I determine the same?

Did you receive a 1099Misc?  It sounds like you are being paid as an independent contractor--in other words, you are considered "self-employed" by the IRS.

Thanks for the quick reply! I haven't received my tax form yet, but yes, I was told that it would be a 1099MISC. What happens in this case?

When you are self-employed, you pay a 15.3% "self-employment " tax  for Social Security and Medicare, as well as ordinary income tax.  You can complete a schedule C to enter any expenses you had for the work you performed.  Depending on how much you earned , you are going to need Self-Employed software or maybe the Freedom Edition if you qualify.  I will put a link for that below.

Any estimated tax payments you have been making need to be entered on your 2017 tax return so you get credit for those payments.  You will go to Federal>Deductions and Credits>Estimates and Other Taxes Paid>Estimates

FREEDOM EDITION

You cannot enter a 1099Misc or self-employment income when you are using the Free Edition.  If you qualify, there is another free software program available from TurboTax which will allow you to enter self-employment income.

Try the Freedom Edition: 

https://turbotax.intuit.com/taxfreedom 

You qualify if your income was $33,000 or less, or $66,000 or less if active duty military, or if you qualify for Earned Income Credit

https://ttlc.intuit.com/questions/2026912-how-do-i-switch-to-turbotax-freedom-edition