If it's in /etc/fstab, then it will mount at boot.
As only root has write permissions,
you'll need to modify it so that the user has those permissions.
The best way is:
chown -R user /mnt/point
where user represents your user name (or user ID),
and, obviously, /mnt/point represents the mount point of your file system.
If the root group has write permission as well and you want another group to have it then you can use:
chown -R user:group /mnt/point
If the root group doesn't have write access, then you can use chmod next:
chmod -R 775 /mnt/point
That will give write permission to the group if it's not there and read and execute to everyone else. You can modify the 775 to give whatever permissions you want to everyone else as that will be specified by the third number.
To better cover what you asked in your comment below:
You can add the user option to /etc/fstab, but that only allows the file system to be mounted by any user. It won't change the permissions on the file system,
which is why you need chown and/or chmod. You can go ahead and add the user option so that a regular user without sudo can mount it should it be unmounted.
For practicality, the best option here is chown as it gives the user the needed permissions instantly. The chmod command can be used afterwards if the permissions need to be modified for others.