First, be sure to leave your database on your computer. Just move the images.
Its actually pretty easy. Create a folder on the Synology (either on an existing share or a new one) and make sure you can read/write to it before trying to use it in Lightroom. In LR's Library, go to Folders on the left, click the + and choose new folder. Point it to the folder on your NAS. You'll now have two top level folders listed. Now just drag and drop whatever you want to the new folder within Lightroom. Moving files within LR ensures that your database can find them so your edits are all preserved.
Thanks for the tips. I'll do that when I get it.