You can read the gpEasy documentation for moving to another server. It will give you the general idea of what you need to do. Basically the best way to go about it is to install gpEasy on your new server, see the gpEasy install tutorial. After installing gpEasy on your new server verify that everything is working properly. If everything is functioning properly then the only thing you need to do is upload your data folder from the other server and remove the data folder from your new server. Follow the gpEasy upgrade tutorial for this. Except instead of uploading the "include" folder you will upload the "data" folder. Otherwise it's pretty much the same.
Changing servers in some ways is very similar to changing directories. With a directory you may need to remove the directory from all your internal links, but otherwise it's all very similar.