In the browser (with nothing selected) choose media Manager.
Copy, include render files. DO NOT delete any of the media.
Based media files on existing names.
Duplicate selected items and place into a new project.
Point the Media destination to the new machine (or drive.)
Point the new project to the new machine (or drive.)
This will copy ALL of the media to the 2nd machine - it'll leave the original alone.
Well if you have set up your project properly with all your media kept on an external drive (this is for proformance reasons). Then all you should really have to do is copy the project file from the system drive and then connect your media drive to the new computer.
If you don't have your project set up like this then like has been said use media manager to copy your project to an external and then connect that to the new computer.