celestial mechanics - How do rogue planets orbit around stars in other planetary systems?

Capture of any object is never common. A rogue planet that passes a star will be accelerated by the star's gravity, and provided that it doesn't hit anything will pass the star in a hyperbolic path.

For capture to occur, the rogue planet has to lose momentum, and there are a few ways in which this can happen. The most general way is for the rogue planet to interact with one of the stars existing planets. If the rogue planet passes close one of the star's orbiting planets, it can interact gravitationally, and transfer momentum to the planet, and slow down in the process. This is rather like the reverse of a gravitational slingshot.

It is also possible that a double planet can be captured, if one of the bodies transfers momentum to the other. One of the double planet will escape, the other is captured by the star's gravity.

Capture of rogue planets is very rare. There is no evidence that it has occurred in our solar system (never in 4.7 billion years is a big Never) though some have speculated that Sedna might be a captured object. But we know that captures like this are possible, as Jupiter and Saturn have a collection of moons, some of which seem to have been captured from the asteroid belt.