What is reverse swing?
When the ball is new, it swings on either side because of the shine. But as the ball gets older, it loses its shine and fails to swing. To make the old ball  swing, players keep one side of the ball shiny while the other gets rough or worn out. Reverse swing is the swing a bowler gets with the old ball towards the shiny side of the old ball rather than the conventional swing a bowler gets. If a bowler is bowling an out-swinger, reverse-swing makes it an in-swinger and vice-versa.

How to bowl reverse swing?
If one wants to bowl the reverse swinging delivery which comes back into the batsman, he needs to hold the ball with its seam point towards the slips. A normal delivery will out-swing with this seam position. But in reverse swing, with the rough side of the ball on the off-side, the shiny side will be on leg-side. Your wrist should be at a certain degree (preferably at 20-30 degree) towards the batsmen. It is very important to not change the bowling style and not alter your action, hold, wrist or any other thing that reveals that you are trying something new. Fast movement of the body is key here.