So I’ve never played the game, what did they change?
Not a lot so far. They've added some stuff, as you would probably expect. For example, all the stuff at the start of the first episode where Joel's daughter goes to get the watch fixed is added for the show. The game starts that night and as far as I recall you never meet the neighbors. However, the scene where they drive into town is damn near 1:1 show to game. Anything with Ellie was added, although some of it may have been from the first game's DLC. I don't remember for sure. I know they're going to show some of the DLC stuff later in the season too, because it was in the trailer.
They changed how Tess dies. I mean, she dies at the exact same point, but it's to FEDRA and not to zombies. Other than that, the second episode mostly follows the game. The intro scene, much like the intro to the first episode, was entirely original.
The third episode has the biggest change. In the game, you never meet Frank (he's already dead when you find him), and the relationship between Bill and him is implied rather than shown. Given that you play from Joel's POV for the most part, that's not entirely surprising. The game does what games do and turns looking for Frank into a fetch quest to get a car battery that leads to combat and a boss fight. I'm assuming the show doesn't want to overuse the "boss fight" thing and will save that particular encounter for later in the season.
I think that both formats did something that worked for them. In a game like The Last of Us, you need to keep the player engaged, and you do that by funneling them into action sequences every so often. The show doesn't have that problem, and in fact needs to flesh out the world and characters more, because you can't have a show where Joel spends 90% of the time sneaking around, crafting shivs, and looting cabinets. So they took the same encounter and turned it into a character piece that reflected on Joel and will have a significant impact on his actions going forward. Both ended up in the same place with Joel and Ellie getting the car battery and moving on to the next leg of their journey.