Before you start, make sure the operating system you want to upgrade to will work on your computer.
General steps for operating system upgrade.
A. Save data files and program settings.
B. Make a system image aka duplicate if possible. (requires special software)
C. Get list of installed files.
2 Get operating system.
1, Download new media. (up to several gigabytes.)
In some cases this could take several hours.
2. Burn new operating system to media.
3. Install operating system,
B. Ipxeboot. (MSWindows may require a special server, but Linux and BSD do not)
1. Boot with minimal media. (i.e. floppy, usb stick, or minimal cd)
2. Downloads and installs minimal OS for install control.
3. Downloads and installs the rest of the OS at the same time.
(optional on some OS's you can install a basic system and finish the install
3. Configure system.
4. Install any additional software third party or from OS vendor as needed.
5. Restore any data and settings if possible.
6. Back up to a new system image.
7. Test system
9. Make adjustments if required.
If you made that original backup, you can always restore the system back to the way it was if your new OS fails.
Examples of ipxe boot installs for linux http://www.instructables.com/id/Linux-hints-II/