For this, your TV should support mirroring. You can check it on the TV guide. This essentially mirrors the content displayed on your smartphone or tablet on the television screen. You would not have to connect internet to TV directly, but only to your smartphone.
If your smartphone/ tablet does not have a mirroring feature, you can download an app for the same. Now all you need to do is connect the device on TV, and you are good to go!
Chromecast is another way to go about it. It is a device that connects itself to the TV and then connects itself to the apps already present in your phone/ tablet.
The unique quality about Chromecast is that it beams content from a device to the TV wirelessly. You can directly watch Netflix or YouTube from your phone.