this assumes you are already running a relatively stock install of WP 1.x, where x is less than 2.
# back up the folder where you have WP installed on your server and back up your database. there’s a script floating around that’s supposed to be a one-click solution for WP database backup, but I found it easier to go into phpmyadmin and use its export feature. (copy the results into a file and save it with your old WP install.)
# download the latest version of the 1.2 beta; unzip it into a folder.
# open your current wp-config.php file and wp-config-sample.php in the new version. copy the settings from wp-config.php into wp-config-sample.php and save wp-config-sample.php as wp-config.php.
# delete the contents of your current WP folder on your server.
# copy the new version into that folder.
# run upgrade.php.
# delete upgrade.php and install.php.
# go to the administration interface -> options -> miscellaneous and copy the .htaccess instructions. create a new .htaccess file and upload it into your WP folder on your server.
# tweak your templates as needed. I found that I could just copy my old index.php into the new install and everything worked just fine, but YMMV.
I think that’s everything.