Update, December 2019: installing third-party scripts or package managers which run on boot may overwrite the file /etc/rc.local which I initially recommended using. I've revised this article to recommend a better autostart script directory; feel free to borrow the simple start/stop script I included at the end of this post.
I recently purchased a Synology NAS running DSM 6, and sharing directories via FTP is easy. In Control Panel, make sure the Shared Folder is defined, then using File Station, define access permissions (read, write, execute) for each group or user.
If you want an additional user for FTP access, you make your user (or make a group then add your user to that) then Allow access to the FTP application inside Control Panel -> Users or Groups. The permissions are inherited, UNIX style, to effectively restrict rights over folders and their files.
So far, so simple; this works great for everything on the NAS' internal storage, because by default it uses EXT4 filesystem which supports file & directory permissions and ACLs. On the terminal, a plus symbol at the end of an ls directory listing denotes the file or directory has additional ACLs applied, which can overrule standard UNIX permissions.
However, on any external drives connected to the Synology, for example a large USB3 drive for temporary storage of additional material, those drives may use file systems other than EXT4 so they're accessible by, say, Windows PCs. In this case, given we're probably also dealing with very large files, exFAT is a sensible choice - and the Synology does support exFAT, albeit there's a long story about that. tl;dr - pay $4 and just get the official exFAT Access package from Synology through the Package Manager, it's zero-hassle and has full read/write support. More info on supported external devices here.
One thing exFAT volumes lack when used through the Synology is support for any UNIX file and directory permissions. Normally that's acceptable, but if you're sharing files to other users, either via NFS, SMB or FTP, you may wish to use permissions to prevent accidental deletion - and on an exFAT volume, this means you can't.
But we can do read-only access with exFAT! It just requires some creative thinking...
Click to read the article and find out how