You want to install and configure Samba. I will assume you are using Ubuntu Server 12.04. If you have a desktop installed there may be all kinds of GUI configuration tools you can use but let's keep this simple.
This should install Samba if you don't already have it:
sudo apt-get install samba
Now you should have the file
/etc/samba/smb.conf so edit this and add these lines to the end:
path = /home/username/backup
writable = yes
guest ok = yes
read only = no
Now read the new configuration by running this command:
sudo service smbd reload
Finally, make sure
/home/username/backup exists and is readable and writeable by everyone:
chmod a+rwx /home/username/backup
You should now have a working share. If the IP address of your server is 192.168.0.2 you could visit
\\192.168.0.2\backup from Explorer and see the directory and read and write files.
Note that there is no security here. Anyone on your LAN can access your files. But this should get you started.