You can only (directly) connect a 'smart' TV to the internet (and then only to use the apps which are installed on that particular TV model).
So have you actually got a 'smart' TV? (Model number, please? It will be on the box that the TV came in, in the manual for the set and on the back the TV itself).
If your TV isn't already 'smart' you can make it so by attaching any suitable device. (The apps you get vary between devices). For example a Now TV box, for just £14.99, has apps which will allow you to watch Youtube videos via your telly, get music from Spotify and access catchup services (such as BBC iPlayer, etc). If you subscribe to one or more of the optional services you get far more through it. (Foe example, £6.99 per month gets you additional channels, such as Sky 1, Sky Atlantic, Sky Living, Gold, National Geographic, etc).