A:
The Smart TV connects to the internet via via your home Wi-Fi the same as your tablet or smartphone do when at home. You can install apps on the TV the same way that you do on your smartphone although there are fewer apps available. For instance, you can install Crackle or Netflix Samsung smart TV's in which case you don't need anything else other than an Internet connection and the app to stream movies.
If you have a tablet running KitKat 4.4 you probably can also use screen cast which will cast anything playing on your Android tablet to your TV (picture and sound). Some tablets also have an HDMI out connector which is another way to use your TV's screen and speakers for streaming content.
I'm not sure of the actual internet service you have based on your description of running through a phone jack. I assume that you have DSL from the phone company and most if not all of their DSL modems have built in Wi-Fi. If you want to do what I have described above you will need a home Wi-Fi router which you probably already have.