How do I file taxes as a freelancer? My existing Turbotax account for non-freelance work doesn't have an obvious way to move forward with this.

Sorry--you cannot use the Free Edition for free lance work.   If you are a free lancer, you are self-employed so you have to prepare a Schedule C and pay self-employment tax for Social Security and Medicare as well as ordinary income tax.  The Free Edition cannot prepare a Schedule C.   You might be able to use Free File---- which is a different free software that can do a Schedule C--if you are within the income limits.  Otherwise you will need online Self-Employed or any version of the CD/download for the forms and schedules you need.

Try Free File: 

You qualify if your income was $39,000 or less, or $72,000 or less if active duty military, or if you qualify for Earned Income Credit

https://ttlc.intuit.com/questions/1900583-what-is-turbotax-free-file-program

• https://ttlc.intuit.com/questions/2026912-how-do-i-switch-to-turbotax-free-file-program

Note:  If you do not qualify to use Free File then you will have to upgrade to Deluxe or higher in the paid versions of the software.   

 Online Deluxe $60  State software $50

Or—-Use this IRS site for other ways to file for free

https://apps.irs.gov/app/freeFile/

https://ttlc.intuit.com/questions/2903027-how-do-i-report-income-from-self-employment

https://ttlc.intuit.com/questions/2926899-how-does-my-side-job-affect-my-taxes

https://ttlc.intuit.com/community/self-employed/help/what-is-the-self-employment-tax/00/25922

https://ttlc.intuit.com/questions/2902389-why-am-i-paying-self-employment-tax

https://ttlc.intuit.com/questions/1901340-where-do-i-enter-schedule-c

https://ttlc.intuit.com/questions/3398950-what-self-employed-expenses-can-i-deduct