Tesla have historically provided all cars with premium connectivity without them realising, but from 2019 they have introduced this as a subscription model for some owners. The subscription provides the capability to access some of the car’s features over cellular/mobile networks.
Irrespective of premium connectivity all Teslas come with Standard Connectivity. This allows the cars to receive limited software updates over-the-air (although the general advice is to connect to your home wifi for the fastest updates). The more relevant features are basic navigation features, Bluetooth connectivity to your phone, Radio (not digital radio) and MP3 music. You also have remote app connectivity to the car. Essentially you only get over the air are essential features.
If you opt for premium connectivity the car will get more frequent over the air updates (although still see the point about home wifi being the best option), Satellite imagery on the map, and media services such as Spotify or Deezer depending on region and streadming radio via services like TuneIn.
For cars that have the necessary hardware (ie M3 and MS and MX with MCU2), services like Caraoke are available.
Essentially, and service that is not mandatory for the core driving features of the car are only accessible over the air if premium connectivity is selected.
Premium connectivity can be obtained without the subscription by using your phone as a mobile hotspot. The downside to this approach is the car will drop the wifi connection as soon as it is put into D and you will need to reconnect. Its pretty clunky but if all you want is some services while charging, its an option.
Cars ordered in the first half of 2019 get it for the life of the ownership of the car (not the automatically for the life of the car). Tesla and dates are a little hazy as order and production dates can vary especially away from the US where delivery timescales can be some time, and buying from inventory can result in a car made before the dat having it even if bought after the date.
Tesla since the beginning of January 2020 will remove it from any used car they sell, including cars they sell through auction to dealers. This is the same approach they take to free supercharging that some cars originally had for the life of the car, but have subsequently had it removed. Tesla currently only do this when they are the owner of the car, even if that ownership is brief following a lease return sent to auction.
New cars come with a free trial period, the length of which varies depending ont he model. After that its about $10/£10/10Euro as a guide.