I was up a piece but could not win. What went wrong? I lost this game and I am not looking for a computer analysis, but what approach should I have taken instead? The game continued 1. Rxd4 Rb7 2. Rxc4 dxc4 3. a4 b4 4. Bd4 Rd7 5. Bb6 c3 6. Rb1 Rd5 7. Kf2 c2 8. Rc1 b3 and I lost.

 [FEN "6k1/r4pp1/4p3/pp1pP2p/2rn1P2/4B2P/PR4P1/3R2K1 w - - 0 1"]

 1. Rxd4 Rb7 2. Rxc4 dxc4 3. a4 b4 4. Bd4 Rd7 5. Bb6 c3 6. Rb1 Rd5 7. Kf2 c2 8. Rc1 b3
You unblocking your opponent's passed d-pawn with 2. Rxc4 is what went wrong from a pragmatic perspective.

You are up a piece.  The only way black wins this position is by promoting pawns so that you're not up a piece anymore (e.g. pushing that 2-to-1 queenside pawn majority).  

This can be easily stopped with the following approach:


Keep your rook where it is.  It's doing a fine job blockading the passed d-pawn.  Ideally, you want a knight to blockade the pawn, but the rook can do this as well.
Bring your last piece (i.e. the king) over to the queenside to make sure those pawns don't go anywhere.  They shouldn't since you have two rooks, a bishop and a pawn there already.


Try following the above advice by playing it out against a comp.