Every recent Tesla has a built-in LTE connection. (I think some of the earlier models were 3G only)

You don't need to buy your own SIM - it comes with its own international roaming SIM, with free data for 8 years.

What happens in 8 years? Do you pay Tesla for a subscription?

Minor correction, it's free for 4 years.

As for what happens, nobody knows, because nobody's run out the four years yet. When they announced the four free years, they also said that the clock started for existing customers on January 1, 2014, so nobody will hit the end for another year and some.

I'd guess that it'll end up being a paid subscription after that, but nobody really knows yet. I wouldn't be surprised if Tesla doesn't know yet. I wouldn't be too surprised if they just make it free for life, since it's pretty cheap to provide and so important to the car, but that might just be wishful thinking on my part.

There will be a cost, but it will be minor, to offset their data costs on ATTs network for the massive amount of data they using for autopilot telemetry.

There is a rumor their cellular costs far exceed their Supercharger electricity costs.

I wouldn't be surprised if that last part was true. With my electricity costs, I pay about 4 cents per mile. If that's typical, and if the average Tesla driver does 1,000 miles/month with 10% on Superchargers (which I think is vaguely close to the truth) then the electricity costs would be something like $4/month/car.