How do i find a CPU Cooler that fits to my system?

Your MB is a LGA1156 socket so you'll need to find a cooler with the correct brackets and whether you wish to use air or water to cool it is up to you. You'll find many solutions and many types of both systems so it's really a matter of how much you wish to spend and water in general will give you better cooling

Yes any cooler that fits it will do but you'd want something better than what you currently have so it still depends on your budget and the more you spend the better hardware you'll usually get. It's worthwhile doing some research online once you decide which one is within your budget and see what others say about the performance of the cooler. I could list 100's of coolers but without knowing how much you wish to spend it's a waste of time

A better cooler is always worth it and you can always add extra fans to your system if it gets too hot unless you're already at full capacity in which case a better case can help. You'll find many tutorials on YouTube showing step by step how to change a cooler for most motherboards and it's not that difficult as long as you take the necessary precautions such as disconnecting the power cable from the computer and discharging any current in the system by pressing the power button for approx 30 secs after disconnecting the cable as well as earthing yourself while working on the motherboard

Here is a tutorial and the procedure is similar on most motherboards and sockets
https://www.youtube.com/watch?v=EB6ENUPObLo

It'll tell you in the packaging as well as once you decide which one it'll tell you in the product description online such as the one below and scroll down and look for Socket Compatibility entry

Be Quiet! Dark Rock PRO 3 CPU Cooler [BK019] - $99.00 : PC Case Gear