The Chromecast is a nifty little device. If you don't have one at home, you may still be able to cast YouTube and Netflix to your TV using the open-source DIAL feature.
DIAL, which stands for Discovery And Launch, was created by Netflix and YouTube originally used by the Chromecast to cast videos on your TV. What most people don't know is that DIAL is still built into many Smart TVs. That means if your TV has a Netflix or YouTube app, you might be able to cast videos in the same way: just open YouTube or Netflix on your phone, find a video and tap the cast button. If your TV shows up, you can tap it to cast that video to your TV.
It only works with Netflix and YouTube, and it isn't available on every TV (I couldn't find the option on my Samsung Smart TV), but Chris Hoffman at the How-To Geek explains that most Smart TVs should have this option, and you don't even need to turn anything on -- just make sure your TV is connected to the internet and has Netflix and YouTube set up. Plenty of users in this Reddit thread have noted success as well.
So, check out the link below for step-by-step instructions on how to try it out, and see if it works for you!