how to backup hD on to external drive

Connect the external drive. If necessary, reformat it using DiskUtility to MacOs Journaled, Extended.

Go to SystemPreferences, TimeMachine and choose Backup Now.

For more detailed information: click at the link at the top of this page

Using Time Machine is the easiest way.

Format your new drive using Disk Utility in MacOS. If you don't then get a prompt to use it as a Time Machine backup drive, go to "Time Machine" in system preferences and select your new external drive. You should then have Time Machine do a backup then and now. The first backup will take a while, hours probably if you have a lot of data. Future backups are net-change only so they run much faster.

Good luck.