What should I do before changing graphics card?

Have a cup of tea.

But seriously, that's about all you want to do and you don't even need to do that before you rip it out.

Any old-config issues can be resolved fairly swiftly when the new graphics card is in. If you have issues,

• Get to a terminal any way you can (login if it boots to terminal, or try a TTY via ControlAltF1, or if all else fails, hold shift on reboot and enter the recovery console.
• Remove old driver packages
• Nuke /etc/X11/xorg.conf from lower orbit.

These are things you can do before changing but it makes very little difference.

I like Oli's answer. :)

The only thing I might add if your paranoid about picking a new card and want to be extra cautious would be to check the Ubuntu hardware catalog for video compatibility with your specific card choice.