Pulling a cable from your current network location would obviously be ideal, but not necessarily a requirement if all you need is streaming movies/sports.

How far away is it, and what do you already use for wifi? If you don't have crazy bandwidth needs, any mediocre wireless mesh should be able to get you streaming.

If you can afford it (~$350+), one with a dedicated backhaul band would be ideal for easy, reliable connectivity.

I recently did the same.

I went with an omada mesh network. I mounted an AP in the house, a pan in the garage, and an outdoor AP on the side of the house. The outdoor unit was key.

If you run a cable you have to also make sure the two buildings have a shared ground or use fiber optic cable, otherwise your Ethernet becomes the shared ground.

I feel like this question comes up often enough that you may want to search this sub.

rather than reinvent the wheel

https://www.reddit.com/r/HomeNetworking/comments/17nr5j5/adding_internet_to_backyard_shed/

https://www.reddit.com/r/HomeNetworking/comments/8kede8/best_way_of_extending_wifi_to_backyard/

https://www.reddit.com/r/HomeNetworking/comments/17t4dqf/networking_question_for_backyard_office/