I'm using TurboTax Deluxe for the first time. I expected a total cost of $59, but I'm seeing $118 instead - $59 for federal and $59 for state. What is this extra charge?

When you use online TurboTax the fees for federal and state are separate fees.   You posted from online Deluxe--$59 for federal and $59 for the state.

How can I see my TurboTax  fees? 

 

  https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online

 

If your TurboTax fees are higher than expected, you can reduce them by removing add-ons     (BEFORE you e-file) :

 

• Remove Premium Services
• Remove MAX Defend & Restore
• Remove a state
• Remove PLUS Help & Support
• Remove Pay With Your Refund

 

When using the Deluxe online edition, which is currently $59, and you add a state program, the state program is an additional $59.

If you do not want the state tax return then see this TurboTax support FAQ for how to delete the state return when using the online editions - https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/delete-state-return-turbotax-online/L8v9awRbh_US_en_US?uid=lu759efj