This will require a more detailed answer then I have time for now. I'm sure you'll be getting a lot of follow-ups to this.
I would suggest you start with this user tip The Well-Trod Path: a Beginner's Guide to how Aperture's major parts inter-relate by kirby a frequent poster here.
Also make sure you give the User Manual a good read especially the parts about the various parts of the library and how they go together.
regards and welcome to the list
I second Frank Caggiano's suggestions - Kirby's User tip and the Aperture 3: User Manual are great starting points.
1) How to use folders, projects etc? Let's say I made hiking tour for several days, do I make a project for each day or for the whole trip? Or do I just put the several "day-projects" into one folder?
Aperture will have no problems, if you put thousands of images into one single project, but it will be difficult for you. Projects are easier and faster to browse if you keep them small - it would be tedious to scroll through thousands of images. The common recommendation, following Kirby's advice, is "one project - one shoot".
When I am travelling, I create a folder for each trip, with folders inside for each destination, and for each day at the destination a project.
Folders are very convenient to hide and collapse large parts of the library quickly. There is one folder "Family", one folder "Computer Graphics", one folder "Lectures", one folder "Travel". When I am working on "Travel" projects, I collaps all other folders.
2) What are albums for? Just for presentation purposes (e.g. put all photos from the hiking tour that I want to show to my friends into the album and sort bad pictures etc out)?
Albums help you to organize your images for special tasks. Lets say, when you return from your hiking trip you want to order prints for your fellow travellers. You then simply drag the images you want to share with your friends to albums, one album for each friend. Albums do not hold duplicates of your images, they simply reference the image in the project. You can have the same image in several albums.
Albums can be seen as collections of images that are related in some way. If you tag all images showing a tiger with the keyword "tiger", you can create a smart album with all images tagged "tiger", and if you have a keyword "slideshow" you can create a smart album holding all images you want to consider for a tiger slideshow by defining a smart rule: keyword is "tiger" and "keyword is slideshow".
4) When to use dia show (hope this is how it is called in the english version)? Would I put it in an album?
The English term for the German word "Diaschau" is slideshow. When you create a slideshow you start by selecting a preliminary set of images you want to include, and yes, you can do that in an album or smart album, then you select all images and use the command "File > New > Slideshow".
This will create a slideshow album, where you can arrange the sequence of images in a filmstrip, define transitions and titels, and add music clips. You can choose between different themes, from very basic presentations to elabor te presentations with so many effects, that nobody will pay attention to your pictures, because they will be stunned by the effects
5) A book means a physical book which I could order from Apple with the chosen photos?
Yes, a book will create a pdf file, that can be printed as a hardcover or softcover book by Apple, or you can print the pdf on your own. Again you can select between a variety of themes, or use plug-ins to send your book to another printing service.
6) What for is the light table?
The light table lets you compare images side by side. You can arrange and scale them freely in the light table viewer - like on the old "Diasortierpult" used for viewing and arranging transparencies. You can use it to print your layout.
Good luck with your Aperture projects. Feel free to post back, if you have more questions.