it's really non-geek if you follow the instructions to the letter. Fire up Terminal, and type the following line :
sudo apt-get dist-upgrade
There's a way with Synaptics, but trust me, this is waaaay easier.
EDIT : Missed out that OP wanted to upgrade to 9.10, which hasn't been released yet.
Do the above pre-edit answer first to upgrade to 9.04 (just to be safe). Then :
Type in Terminal
update-manager -d
Update Manager should open up and tell you: New distribution release '9.10' is available. Click Upgrade and follow the on-screen instructions.
Best Answer
If you don't have it already, you gonna need a free partition on your harddrive to install it beside your current OS. If you need to create a partition, Windows Seven (if you have Windows 7) allow you to shrink a partition so you'll be able to create some place for Ubuntu.
If you already have it , just go in Updater Manager panel and you'll have an option to upgrade to 10.04 LTS on top of it.
More details here : https://help.ubuntu.com/community/LucidUpgrades#Upgrade%20from%209.10%20to%2010.04%20LTS
Update : (thanks to th3dude )
Could check this out too that outline exactly what I'm talking about :
Update to Ubuntu 9.10 from Ubuntu 9.04