Exporting your Database by creating a Plesk Database Dump
Begin by logging in to Plesk. If you have more than one subscription, be sure to select the correct one using the dropdown at the top of the panel
Under the Websites & Domains tab (default), choose Databases to be taken to a list of all databases.
Look for your database in the list. If you or someone else has tagged the database with its matching domain, it will say: "Related to: " and then show the domain beside it. Use the related to feature to identify which database you want when there is more than one. If the database hasn't been tagged with a domain, you can figure out which database you need by clicking on 1-click web apps, then finding your app in the list. Click the wrench icon, then the files & tables tab -- here it will show you the database name.
Once you've identified the correct database, choose the "Export Dump" option (skip to the phpMyAdmin section below if you do not see an Export Dump option).
You may save your dump to the Root directory, as is selected by default, or you can change the directory. If you opt to change the dump directory, do not save your export to a web-accessible directory like httpdocs -- this will be a major security risk.
You can leave "Automatically download dump after creation" unchecked if you intend to re-import the database in the future using the "Import Dump" button, but definitely take note of the database name so you recall which one to import. Feel free to check the box and have it download to your computer if you prefer to have a local copy.
When this process is complete, you will have a dump of your database either saved in the server storage location of your choice or on your computer.
Exporting your Database using phpMyAdmin in Plesk
Follow steps 1 through 3 above
Click the "phpMyAdmin" button or "Webadmin" button. Clicking this button will log you in to the phpMyAdmin utility automatically. If neither button appears, check the troubleshooting section below.
Choose the "Export" button in the toolbar across the top of the page.
Simple/Uncompressed: You can keep the export method at "Quick" and the Format at "SQL" and click Go to obtain your database export, however this will not compress the database contents and therefore could take some time to download.
Advanced/Compressed: Choose Custom for the export method and scroll down. All tables should be selected by default -- there's no need to change this. Ensure "Save output to a file" is selected (it should be) and set Compression to Zipped if you're on Windows or gzipped if you're on a Mac or Linux OS (gzipped is often better compression, but files are usually not recognized by Windows without a third party app). Scroll down and click Go. You will now have a compressed full export of your database!