There is no way black can ever attack your two passers, so that should make the calculations a lot easier. So you can just snap up black’s more advanced pawn and then attack the other one. If he defends his pawn, you just advance your connected passers. If he abandons hi pawn, you take it and the. Bring your king over and force your pawns home. There’s not a lot to calculate, really
Calculation

This is a simple king and pawn endgame. Firstly you can see that whatever black do, you can take that pawn on d3. Connected pass pawns can't be taken by the king because if the king take the pawn behind the other will promote. The plan here is take the pawn then push the pawn and always keep them close together, then take the other pawn as the black king has stop your pawns then bring the king to help. This is a common strategy in endgame like this, It's applicable in rook, bishop or knight + pawn endgames
The easiest way is to block the d3 pawn and there's nothing black can do. If he pushes, you push. Mind that the black king alone cannot capture your pawns, he can only block them, so there's nothing to be afraid of if he heads toward your pawns. He either has to give up the d3 pawn or to step out of the h-pawn's square.
But generally speaking, no, there are no rules to help you, pawn endgames ARE calculation. For example, if in your position black pawn was on d4 instead of d3, then what I said wouldn't work and it would be a draw.

As soon as you see that black cannot protect d3 pawn and black cannot do anything with white pawns then the rest is easy.

This is an easy win. Capture the undefendable d pawn, put your king in front of the b pawn and advance the connected passed pawns. Should black try to advance his b pawn your kingside pawns queen easily. Should black rush to head off the kingside pawns just capture his pawns and bring your king over to force a queen.
The main points are that a king cannot capture two connected passed pawns as long as they stay together in a formation such as they are in this position--if the king captures the rear pawn the advanced pawn wins the race to the eighth rank. Also, K + 2 connected passed pawns cannot be stopped by a lone king. Once you know these basic endgame principles the solution is obvious immediately.
So the key is to know endgame technique. Good endgame books are easily available. Endgame theory doesn't change the way opening theory does so what you learn studying endings will still be useful 30 years from now. The most frequently seen (therefore most important) endings are K + P and rook endings. Knowledge of these endgames will not only allow you to win (or draw if you have the worse position) a lot of games that you might otherwise draw (or lose), but will help you in the middlegame. Knowing when a plan you are considering will produce a winable endgame helps a lot. It also lets you know when to avoid simplification.
Black to move
I was playing white. It was a winning position for white, but I took 15 minutes to calculate the correct reply to each of black's moves. This was fine as it was a daily game. But, are there any short cuts to calculating a position like this? Methods similar to the rule of the square? Cause I can't take 15 minutes to calculate one move if this were a 30 minute game.