So, you're wondering how to build, modify, blow up, or just play around with some of the stuff available here; that's great!
Take a look at each project's page and you'll find a bunch of stuff, CAD files and gerbers for manufactuing PCBs, source code and binaries for projects with microprocessors, and full documentation for putting it all together.
If you just want to get one of the projects up and running as fast as possible, download the Gerber files and use them when ordering PCB's from somewhere (like Itead or Seeedstudio).
So what about the components? Download the documentation for the project and you'll find both a bill of materials in the PDF file, as well as a spreadsheet file with pre-selected components from Farnell and Microkit (Sweden only). Enter the number of boards you're going to build, copy and paste the order information in Farnell's/Microkit's quick order function and simply order the parts!
If all goes well, after a few weeks you'll get both bare PCB's and components. Now the manual comes into use, it completely describes how to assemble, configure and use the project. Now, if there's something you don't like or something you'd like to change that's fine, because all the source files are completely available on the project page under an OSHW license — just download the CAD project files and/or microcontroller source code and hack away.