How do I put in for a deduction for additional income (side job) for things like supplies, travel fees, etc?

Sounds like you are referring to self-employment income from a "side gig"---and indeed you would have to upgrade to  online Premium to enter expenses on a Schedule C, or you could use any version of the CD/download to enter such expenses.  You cannot prepare a Schedule C with online Deluxe.

Or—-Use this IRS site for other ways to file for free.  There are 8  free software versions available from the IRS Free File site

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

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

https://ttlc.intuit.com/turbotax-support/en-us/help-article/form-1099-nec/1099-nec/L5qTsBiSe_US_en_US

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

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

https://blog.turbotax.intuit.com/self-employed/self-employed-tax-deductions-

calculator-2021-2022-50907/

https://ttlc.intuit.com/questions/1901110-do-i-need-to-make-estimated-tax-payments-to-the-irs

https://turbotax.intuit.com/tax-tools/calculators/self-employed/

Yes, if you are using TurboTax Online, you have to upgrade to Premium to deduct business expenses.

I am assuming that you have a 1099-NEC for your side job. If you have a W-2 for your side job, you can't deduct any expenses related to your work at all. 

If you want to switch to the Desktop product, which you install on your computer, you can include self-employment income and expenses in the Deluxe version. Follow this link for more about that.