I have seen the work of many photographers and I am wondering how they manage to create such amazing compositions. I have tried to watch tutorials on youtube and recreate some great ideas...the result was far from theirs even though I have followed every step.

Is photography a skill you can learn? Can I become a good photographer if I practice long enough? Or it is a talent you need to be born with? 

I've never met one photographer who had talent alone. Sure you can find a few talented kids taking pictures but each professional photographer I ever met had many hours of trial and errors. It's a learning curve. 

I am a photographer based in Budapest, Hungary. I have many years of experience in this field and I can tell you, the only things you need in this job is time, passion and a good camera. You need to learn how to set up your camera, how to use different features such as exposure or ISO. You need to learn how to use software to edit your photos. Photoshop and Lightroom can be your best friends in this adventure. You also need to learn about lights. You need to learn to make the most out of natural lighting, and also start using artificial lights as well. It is a lot of theory that you need to study as you can see. 
Talent, sure, is important. Talent is always a plus. But talent is not everything. You need to have a lot of knowledge and you can learn how to shoot the best pictures by knowing all these technical things.