Hi, the basic steps would be:
1. Install DSpace on the other server by following the install guide:
https://wiki.lyrasis.org/display/DSDOC5x/Installing+DSpace Make sure it's working with no content.
2. Move over the content. This involves moving the [dspace]/assetstore folder (where all the files are) and the entire database contents from the old location to the new location.
* Moving the [dspace]/assetstore folder would just mean copying all the contents from one location to the other.
3. Run the database migrate script ([dspace]/bin/dspace database migrate) from commandline. This just make sure your database has been fully updated based on the installation you are running.
4. Reindex all content into Solr ([dspace]/bin/dspace index-discovery -b) from commandline. This makes sure your search/browse works correctly with all the new content you moved over.
At this point, everything should be working. But, if you hit issues or have more questions, let us know on this list. I do recommend trying a "test" of this process first to get comfortable with it & make sure you don't hit any issues along the way.
Tim