I am new to Linux (Ubuntu 10.4 LTS on a Thinkpad T40), now just two days, and had everything working nicely. But since I wanted a better higher resolution I tried to set the monitor resolution to a higher value. After selecting a higher resolution first the screen went black and now it has a white background and is steady but has flickering areas. The system is still working. How can I go back to the resolution that was working?

It sounds like the display has been set to a value beyond its native resolution. If that's the case, then you probably have a couple options.

1) If there's a safe-mode you can boot into (say when GRUB loads), try and use that and then change the resolution from there.
2) Use the Ubuntu disk as a rescue disk (on the assumption this is possible---not being an Ubuntu user I don't know what tools you have immediately on hand).
3) You could reinstall Ubuntu from scratch.
4) And if you're feeling adventurous, boot into the command prompt and edit /etc/X11/xorg.conf, removing the offending display settings and replacing them with lower values. (The section you'd be looking for is "Screen". The display modes will be below, one line for the available colour depths.)

Thank you for your suggestions. I actually rebooted twice not doing anything and it resolved itself.