As you progress through the game post- Dragon Rising, dragons will periodically appear in the skies overhead- usually they will circle a few times, then head off to wherever they’re going to lurk.  And it’s up to you to get rid of them... by slaying them.

One of the earliest dragons to appear will head over to Whiterun to attack.  Like Mirmulnir, this one breathes fire- but unlike Mirmulnir, it doesn’t have a single tower to orbit- it’s got a whole village to terrorize.  This actually, as it turns out, is a good thing.

For this fight, you’re going to want to have a long-range attack- a second-grade Destruction spell or a bow are your real options here.  Standing on the steps in front of Dragonsreach gives you an overview of the merchant area of Whiterun, which is where the dragon is going to start out attacking.  It likes landing on the roofs of buildings and belching flame down at the unfortunate people below- who will mostly be the guards that are fighting it.  As long as you stay well back, you can join the Whiterun Guard in peppering the creature with arrows and not attract too much of its attention.  It takes a little time and can be a little harrowing if you’re worried about your favorite Whiterun villagers, but everyone should be secure in their houses fairly quickly, leaving you and the guard to wear down the dragon.

By the time the dragon is injured enough to land on a more permanent basis, you’ll want to be on the walkway that leads to the front doors of Dragonsreach.  This is entirely because of the dragon’s breathweapon.

When the dragon lands on the ground, the guard will crowd around it and start beating on it, drawing its attention.  From there, it’s very like your fight with Mirmulnir, though this dragon lands while it’s still got a lot of life left, so it’s harder to just charge up and cut open its flank.  For safety, you’re going to want to stick with ranged attacks.

If you followed advice and stuck on the Dragonsreach walkway, though, the dragon will either be penned in by the wall around Dragonsreach, or hemmed out by it.  This is where you take rampant advantage of terrain- as terrifying as the flaming breath is, it won’t penetrate stone, so you can use the wall as cover, ducking behind it every time the dragon tries to blast you and then peeking out to shoot it a couple of times.

If you’re more melee focused, this gets a bit difficult, but you should be able to get by if you wait for the guards to draw the dragon’s attention, then rush around behind it.  This becomes vastly easier if you’ve already seen the Graybeards, as the Whirlwind shout will launch you into position rather suddenly and keep you out of the dragon’s face, which is really the most dangerous part of it.