I don't know which Linux distro and version you are using and whether you are talking about an external (removable) drive or an internal one.
For removable drives, on recent distro versions, policy-kit is used to enable the desktop user to the media. There is a similar policy for fixed media. This is how auto-mounting of pen drives works.
For fixed media, a root user can edit /etc/fstab so that is mounted when you boot up. After that it doesn't need to be mounted by a regular user.
If the /etc/fstab entry uses the "user" or "users" option and the "uid=" value is set, then a regular user can mount that partition. ( This is for systems where the mount command is suid root ) The "mount" command checks for a uid= value. For removable drives, the first column in the /etc/fstab file should be a unique identifier for the filesystem.
The uid, gid, fmask and dmask mount options determine the permissions of a HFS, FAT32 or NTFS filesystem. The permissions of all files will be the same.