You need to copy the files over and also copy over a backup of the library so you do not have to do your setup all over again.
If both computers are on the same network, you can just copy the music files (flac, wav, mps, etc.) from one computer to the other, e.g. using Windows Explorer on a Windows system. From the new computer, just look under Network in Explorer to find the other computer. Just copy the whole music file from the old computer to the new one. You will have to allow sharing on the directory the files are being copied from on the old computer. The copy may take some time depending on how many files your have, but it is very straightforward. If you can plug them both into your router the copy will be much faster than over WiFi. If possible put them in a folder of the same name as on the original computer
Alternatively, you can transfer the files from the original computer to a USB disk drive and move that drive to the new computer. Again, if you can use the same path name (device, folder) it will make the setup easier.
To move your J RIver library to a new computer, do a backup from within J River (File - Library - Back Up). Put that file in a directory you can find. Then copy that file to you new computer, and do a Library Restore from within J River. That will copy all you tags, settings etc. to the new computer. If you can use he same directory for the music files on your new computer as on your old one, everything should just work. You can move the backup file to the new computer over the network or with a USB drive, just like you did the music files.
If you have a different directory on the new computer you can use Tools - Library Tools - Rename, Move & Copy - Find and Replace to change the path. If you do the Find and Replace, I would suggest trying it on an album or two first, before doing the whole library.
Any questions, please ask. I do it fairly often.