There’s a good chance you can watch Netflix without any external device. Most, if not all, smart TVs will have a Netflix app either pre-installed or one that can be downloaded.
If the app is pre-installed already, you just have to find it and run it. There should be a button that takes you to a TV’s smart menu (on a Samsung, for instance, it’s the brightly coloured cube thing). Here you can either choose to run the app and then, when prompted, enter in your email address and password.
If the app is missing or you can’t find it, you can try to search for it if the smart TV has a search function. Failing that, head to your TV’s app store and then search for Netflix. Once found, choose to download and install.
Now either run the app there and then if you can, or go back to where you would usually find pre-installed apps and fire it up.
One important point to note. Netflix requires a broadband connection of a certain speed, otherwise it will pause a lot. But more importantly, ensure your TV is connected via an ethernet cable (the one you stick into a router) or WiFi (smart TVs tend to have wireless connectivity built in). No connection, no ability to download the Netflix app or watch it.