Suppose your /home partition is /dev/sda5 with a size of 10 gig but you have used 9.75 gig of space. Now lets suppose you can create a new 20 gig partition on your hard disk. You could mount the new partition on a temp location lets pick /mnt/home for /dev/sda12. Now as the root user, you can use the following commands to copy your current /home to the new partition /mnt/home.

cd /home

find . -print | cpio -pv /mnt/home

Once the copy is finished you edit the file /etc/fstab and change the /home partition from /dev/sda5 to /dev/sda12. You can restart your system to change the mount to the new location.

You will now find you have 20 gig of space in /home.

Lets have a look at the file system as a picture.

Most of the time a Linux system will mount a memory stick automatically when you connect it to the computer. But what do you do if the system does not automatically mount a memory stick.

Here is a link with more details about the File System. Specifically it will explain more about Superblocks, file system types, inodes and links. This is more advanced than beginner information but is useful if you want a more detailed look. Explore Understanding UNIX / Linux File System

The first understanding is the different types of rescues. Let me give you a few examples.

1. You accidently deleted a file from your home folder.

This is the easiest type of recovery.  All you need to do is go back
to your last backup, locate the file and restore it.

2. You had a corrupted disk or you deleted a critical folder in the operating system.

You need to go back to the installation media and recover the
files you need.  To do this you want to follow the instructions
from the operating system restore process.

3. Your hard disk failed and you lost the whole system.

Once you replace the hard disk you are going to need to reinstall
the operating system, then restore your applications, and finally
restore from your backup.

Before you do a backup we need to decide what we need to put on the backup media. The idea is to backup only the parts of the system which you can not restore from the install CD. The reason for a selective backup is to both save space on the backup and to make the backup faster.

We have two sets of files to backup. To start we need a backup medium. For this example I will use a memory stick formatted as vfat, located at /mnt/usbstick and we will assume this script is being run manually.

#!/bin/bash
# Backup script of /home/john files to a memory stick at /mnt/usbstick

echo -n "Is the USB memory stick mount at /mnt/usbstick ( Y or N ): "
read ANS
if [ lc( $ANS ) eq "n" ]
do
        echo Please insert the memory stick into a USB slot. Press return to continue.
        read ANS
        sudo mount -v -t vfat /dev/sdb1 /mnt/usbstick
done

DATESTAMP=`date %Y%m%d`

cd /home/john
tar czvf /mnt/usbstick/home-backup.${DATESTAMP}.tar.gz ./.bash \
./Document ./Downloads ./.emacs ./house ./Music ./.ncftp \
./Pictures ./.ssh ./transfer

# flush the buffers onto the memory stick.
sync ; sync

# Unmount the USB memory stick.
sudo umount -v /mnt/usbdrive

echo "You can remove the Memory stick now"
exit 0

This script till mount a USB memory stick, change directory to the /home/john, then use the tar command to create an archive. Since we are including the DATASTAMP in the file name each backup will be unique unless you decide to do more than one backup in a day.

If you would like you can use the zip command instead of the tar command by replacing tar czvf /mnt/usbstick/home-backup.${DATESTAMP}.tar.gz with zip -r /mnt/usbstick/home-backup.${DATESTAMP}.zip both archive programs are installed in Ubuntu.

In the past it was common to use magnetic tape to backup a hard disk. The reason was that tape was cheap and reusable. Tape can still be used but these days there are more options.

This is not intended to be a complete list but just a couple of suggestions