I bought a Roku device and should get Apple TV free for three months. How does this get applied?

This forum is for Apple TV hardware, I'd suggest contacting Roku about their promotion and ask how you can redeem it. I'm sure they are not giving away Apple TV for free for 3 month though, you likely mis-typed and meant Apple TV + which is completely different than the Apple TV App or the Apple TV devices.

Read here: https://www.roku.com/en-gb/offers/appletv

You would receive a redeem code from Roku by email.