First thing is first, Reading/Writing/Deleting from a filesystem on a partition are managed by a different set of permissions than mounting a filesystem on a partition. So you will need two fixes, at the minimum, to solve your problem.
Relevant to Both Fixes
inside of the file /etc/fstab there may or may not be a line starting with /dev/sda4. Alternatively there may or may not be a line starting with the UUID of that partition. You can find the UUID by running ls -l /dev/disk/by-uuid and looking for the one that points to /dev/sda4.
If there isn't a line, then you'll need to make one. Either way, the general form of the line should be:
UUID=(hex chars) /mntdir filesystem options 0 0
#or
/dev/sda4 /mntdir filesystem options 0 0
The part of the line you want to focus on is the options section.
Fix #1, Relevant if your filesystem is FAT/NTFS
If your filesystem doesn't play nice with linux permissions, then you can use the umask option to control the type of access to the files. On NTFS-3G, umask=0022 sets the user file permissions to 0755 which is rwxr-xr-x. gid controls what group the default permissions apply to. So for example, you can make a group called ntfsusers and add all users to that group and then set umask=0002 See the Arch Wiki link for more.
#Example NTFS line:
/dev/sda4 /mntdir ntfs gid=users,umask=0002,user,rw,auto 0 0
Fix #2, Mounting the driver as a normal user
The user and nouser options control who can mount the filesytem. When user is present any user can mount the drive. When nouser is present only root can mount the drive. user turns on a few other flags by default, see the link at the bottom of this post.
#Example NTFS line:
/dev/sda4 /mntdir ext3 defaults,user 0 0
Wikipedia on /etc/fstab: http://en.wikipedia.org/wiki/Fstab
Tuxfiles on /etc/fstab: http://www.tuxfiles.org/linuxhelp/fstab.html
Arch-Wiki on NTFS-3G options: https://wiki.archlinux.org/index.php/NTFS-3G#Allowing_Group.2FUser