Let's start with a simple hanging pawn duo position:
A position like this came up in two of my recent games, and being as I lost both times that means it's time for me to take a closer look at the position. The hanging pawn duo is the less appreciate cousin of the isolated queen pawn. Like IQP positions, the side possessing the HPD has greater mobility and chances for attack. Also as in IQP's, the pawn duo can be a target and weakness, and as the game moves toward endgame, the chances favor the side without the pawn duo.
It follows that he who owns the HPD should seek their chances in the middlegame, and that he should try to keep as many pieces on the board as possible to maximize the advantage of mobility. Further, neither pawn should be advanced lightly - this will provide key blockading/attacking squares to the opponent in the absence of other factors. However, a correctly timed pawn advance can be winning, imagine for example the following push of d5:
In this simplified position, the d5 push with a bishop on b2 creates tactical possibilities on the long diagonal. This advance is a constant threat, much like in the corresponding IQP position. There is also the paradoxical c5 advance, creating 'blockaded security' according to Nimzovich in which the d4 weakness can be offset by a strong outpost at d6. It is also of considerable importance for White to control unoccupied central squares (ie e4, e5, and f4 in the top position), as these squares can otherwise be used by Black to launch an attack wither on the White kingside or on the hanging pawns themselves.
The strategy in fighting against the HPD is essentially the inverse of what was just mentioned - exchange pieces wherever possible (as in the IQP); attack the HPD directly, with a goal of luring one of the pawns to advance at an inopportune moment. Fight for control of the unoccupied center squares as a means of attacking the pawn duo. Finally, consider exploding the center at the right moment with a ...b5 or ...e5 breakthrough (vaguely analogous to a hedgehog strategy). Consider a ...b5 push in the following position:
Black gets immediate equality by 1...b5, after which 2. c5 Be6 then 3....Nd5 demonstrates that White is getting nowhere (although Black may be pressed to show an advantage - blockaded security!).
These are the simplified ideas, next we'll look at how to apply (or misapply) them in practice.