WordPress has released an upgrade called 1.5.2 with some security fixes and a few neat new features and benefits, though most of them are under the hood. You can download the upgrade via WordPress Downloads.
In general, follow the upgrading instructions on the Codex, but there are specific instructions here on the WordPress Support Forum, along with a detailed list in layman’s terms of what has been changed and upgraded.
Just to emphasize, because it’s a common mistake, be sure and delete all the appropriate files and folders that need to be replaced. DO NOT copy the new files over. It might work, and it might not, so go the safe route. DO NOT delete the wp-config.php in the root WordPress directory, and anything in the /wp-content folder or any translation folders and/or files. This upgrade does not require running any upgrade script, just delete the old files and upload the new ones and you should be ready to go.