If we can sum up all of Game of Thrones, it would be the simple phrase "oh gods, not now, don't kill me now, shit I'm dead." But, before that happens, people make some friends. This episode is all about making friends, culminating in the ultimate friendship challenge. But we'll get to that.
Four big things happen in this episode. Ned investigates, Dany becomes a queen, Jon makes a friend, and the last scene. For the most part, Dany's is the most straightforward. She's becoming more one with the horse people as they show up at their hometown. Her brother is not, and when he tries that "wakes the dragon" shit on Dany learns that horses beat dragons in that piddly nonsense. Or maybe the dragon has woken after all and it wields a belt and slaps its brother like a little shit. Also, the least we talk about the first instance of "sexposition" the better. I'll never be able to list dragon names in the shower again.
The second least convoluted but more emotionally ambiguous is Jon at the Wall. A new boy has come in, the fat man himself Samwell Tarly. He's a coward and really bad at fighting so nobody likes him. Then Jon learns his backstory, that Sam's essentially a cast out bastard like himself, and defends his new friend from all foes. They are brothers and will stand by each other, even if it kills him.
Then there's the Starks…. Let's start with Ned, I guess.
Ned is looking into the death of Jon Arryn, his friend. He figures the best way to go about this is to do everything Jon did that got him killed. Pushed along by Littlefinger, he visits a brothel, a forge, and a book, which in my D&D campaign would raise up some kind of metal fuck-monster. Ned just gets more questions about Robert's bastards and a threatening visit from Cersei. There's also a bit with the tournament and Jon Arryn's squire (now a knight) being killed, but that's mostly to muddy the waters and get the backstory of the Mountain and the Hound as well as set up Littlefinger being creepy AF to Sansa.
Then there's Catelyn and Tyrion. We get a nice little big with Tyrion and Bran where the little guy gives the little guy plans for a saddle. Rob's a dick, though, because he thinks the Lannister's tried to kill Bran and fair point. Then Tyrion goes to an Inn on his travels and runs into Catelyn. Turns out money doesn't buy friends in the Riverlands, and Catelyn calls up all her dad's friends to arrest Tyrion. Swords out, dwarf busted.
For the most part, this episode was all about fleshing out our locations. Dany is coming into her horselord queen-ship and getting out of her brother's shadow. Jon is learning what brotherhood on the Wall really means. Ned is just, like, "whoa, King's Landing is full of dickheads and spies." And of course, we start a new plot threat with Catelyn and Tyrion on a road adventure. A fun episode full of set ups of things to come.