mitok, I suggest you either purchase a book like Zinn and the art of "Road (or Mountain) Bike Maintenance" so you can see the details of the assembly and get detailed step-by-step instructions.

Doing this job requires either a significant expenditure for the "proper" tools or considerable skill using makeshift ones. I don't know what your mechanical skill level is, but your questions indicate that you are unfamiliar with this part of a bicycle. In your case, I suggest that you take the frame and fork to your LBS and pay them the nominal fee to swap out the fork for you. An LBS generally charges about $20 or so for the labor to replace and properly adjust the headset. You would spend much more than that just on a headset press that you may not use for another year or more.

I do almost all my own bike work but still pay an LBS to swap out headsets.