By driving extremely slowly.
Aerodynamic resistance is key, and it goes up with the square of your speed, so driving slowly lets you go much farther. If you want to set a distance record in an EV, you want to drive around 25-30MPH.
The current record in a Tesla is over 500 miles, while the official range is under 300. Musk's comment was about how ongoing small battery improvements will allow the record distance, driven at 25-30MPH, to break 1000km in the next couple of years.
But all the idiot news organizations out there either misunderstood it entirely or saw it as an opportunity to drum up page views, and are either outright presenting it as a practical range, or are at least not trying very hard to present the real context, as is happening with this article.