First check your kernel version, so you won't delete the in-use kernel image, running:

uname -r

Now run this command for a list of installed kernels:

sudo dpkg --list 'linux-image*'

and delete the kernels you don't want/need anymore by running this:

sudo apt-get remove linux-image-VERSION

Replace VERSION with the version of the kernel you want to remove.

When you're done removing the older kernels, you can run this to remove ever packages you won't need anymore:

sudo apt-get autoremove

And finally you can run this to update grub kernel list:

sudo update-grub

Ouput from df -h

Size Used Avail Use% 
Mounted on /dev/sda1 5.5G 4.4G 786M 86% 
/ udev 996M 4.0K 996M 1% 
/dev tmpfs 402M 880K 401M 1% 
/run none 5.0M 0 5.0M 0% /run/lock none 1004M 156K 1004M 1% 
/run/shm /dev/sdb1 30G 1.4G 27G 5% 
/home /dev/sdc1 299G 31G 268G 11% /media/HD-PCTU2