I happened to be given a decent bike - Trek 1000 - in a good condition. The only problem is that the frame is only 56 cm while I am quite tall so I need ~62 cm. Is it possible to take all the nice parts from the current bike and put it on a new/used larger frame? I think all of the parts should fit the new one, I am just not sure about the fork. I do not know much about bikes neither I ride a lot (at this point), so any advice is greatly appreciated!
This is a very doable project. However, the cost benefit will vary. You need to be very sure of what parts will be reusable. If you are going to pay your local shop to do the work then as @Eric Smekens has said, sell the old one and look for a bike that fits. If you are planning on doing it yourself it is an excellent way to learn how your bike works and how to do your own service. You must consider the cost of the special tools you'll need to buy, and if they will be used enough to justify the expense. Some cost considerations you may not have thought of. You may find some of the bearings serviceable, but not worth paying someone to reinstall them. Some parts may need to be replaced because they won't fit the new frame.