Rook and pawn endgame

I recently played a game where I ended up in this position after I decided to trade down to an endgame because I was sure it was a winning one. Below is the position and I'm still certain it should be a winning position for black. It is black to move. What should I have played to win from this position (because I lost the game by several faulty moves)?

capture the white pass pawn.....Rd7 then Ra7 bring your king to b6...2 pawn up should be an easy win. 

Hmm but I don't see how I can stop him from taking my passed pawn and there is not enough time to make another and queen it before he can defend it. Like this:

1.r-d7 or d-8 to a7 or 8

King then simultaneously attacks the passed pawn and protects yours.

Can you win it from there? 

It should not be terribly difficult for black to win white's a-pawn, but there is some trickiness to it if white brings his king right up into the fight:

 Ah yes now I see it. You're right. The trick is to bring the king infront of your own pawn and not the back side of the pawn.

I might say instead that the trick is using your king to restrict the enemy king's movement. In your example, the white king is unopposed and marches right over to the support of his pawn; in my example, the white king cannot approach his pawn at all. Here's a better comparison to your example, where white does not push his pawn but uses the move to get his king rolling: