Export content types using features I am struggling with it, but I can't do it by myself. Google doesn't gave me links for tutorials other modules doesn't help me too.

I would like to export content types definition from Drupal site to another.

Could someone give me any hint how to do it?
Sure,

Install the features module and then you go to structure -> features

Click on "create new feature"

Give it a name and then on Edit component you can select what you want to export.
Select Content-type: node and you will see a list of all your content types, check the content types you want to export,( when you click the checkbox, you will see the ajax image wait till it disappear) and then click on download feature.
Version 7.x-2.x has got a better UI and it's possible to download it straight into your sites/all/modules/features folder if you give web server permission to write into that folder.

The feature you downloaded works like a module so upload the folder you downloaded into sites/all/modules/features, go to you module page and enable it.

You will find your content type with all the fields.

I suggest you to play with features module to understand all his potential.