The short answer:
Move everything in your cgi-bin and your data directory (if it's not under your links cgi-bin directory). Make sure to download/upload all .cgi or .pl files in ASCII
You don't need any of the built .html pages (except for your template .html files in your /templates directory usually under your links cgi-bin directory). For safety, you can download your most recent backups, but no need to upload.
Change the pahts in links.cfg (and maybe a couple in the .cgi files) and you will be set.
You can always test it before you move too!
(usually by using an IP address until the domain is changed over).