I have seen so much response about the Mountain Lion update slowing down computers. I am updating from Mac OS x 10.6.8. What can I do to ensure the upgrade will go fine? Do I unplug my external hard drive before installing, or keep it plugged in?

Welcome to Apple Support Communities

There's no reason to think that Mountain Lion will slow down your Mac. Just make a backup of your data before upgrading with Time Machine > http://support.apple.com/kb/HT1427

Also, check that your apps are compatible > http://www.roaringapps.com Upgrade them to a compatible version or delete them before upgrading.

The external drive won't make the OS X Mountain Lion installer fail, but it's better to unplug it during the upgrade.

iWork '08 is compatible with Mountain Lion. iWork '09 includes OS X Mountain Lion features and can be purchased at the Mac App Store.

To upgrade to OS X Mountain Lion, I recommend at least 4 GB of RAM. You can check how much memory you have in Apple menu > About this Mac

I recommend you to install 4 or 8 GB of RAM at least. You can buy more RAM at OWC or Crucial > http://www.macsales.com Depending on the amount of memory you install, it will cost more or less