How to counter opponent formations?

Basically I think that a possession, 4-5-1 shape can be fought off by a counter attacking formation (or that's how I think). What about the other formations and play styles? How can we effectively combat them?

I think this is really hard. It depends on formations, playing style, players and the opponents roles. And sometimes things just don't work out.

The question is far too broad to give a basic answer. It all depends on your own set up, the players, the oppositions players and shape, their settings, the weather and more importantly what is actually happening in a game. There is no set answer because there are many ways to do things and many, many, many, many different variables that need to be took into consideration in the right sort of context.

Basically I think that a possession, 4-5-1 shape can be fought off by a counter attacking formation (or that's how I think). What about the other formations and play styles? How can we effectively combat them?

What do you mean by "counter attacking formation"? Surely you mean style, but anyway (as has been said) the concept is far too simplistic. For example, there's little point in playing counter attacking football against a team that is playing for a draw, irrespective of what formation they're using.

You could try to mirror oppositions central midfielders' shape. For example, if they play 4-5-1 or 4-1-4-1, you could set your midfield triangle in 2-1 arrangement (2 cm and 1 am). Take a look at Milan - Juve game last weekend, it might give you some ideas. Of course you must take into account oppositions shape, mentality settings, roles and duties...