First of all we need to know the uid (user ID) of our user. Open a terminal and give this command:

id -u $USER

This will output a number(usually this will be 1000). Keep this number and let’s go to the next step:
Set fstab to mount the disk as the current user

First of all open the /etc/fstab configuration file as root:

gksu gedit /etc/fstab

You will see something like that:

UUID=3C1850B51850703E /media/disk vfat defaults 0 0

Change the defaults to this:

UUID=3C1850B51850703E /media/disk vfat user,uid=1000,utf8 0 0

Where 1000 is your actual userID. We are done, now every time you login the disk will be accessible from your account. In case your disk is NTFS this wont work, but there is another solution which is actually the simpler one:
Configuring through graphical interface

Install ntfs-config by clicking here, or by executing the above command:

sudo apt-get install ntfs-config

Then execute the program by executing:

gksu ntfs-config

Click on both the options, and you are done