Using an FTP program like FileZilla, connect to your blog host (GoDaddy, BlueHost, DreamHost, etc.) with your FTP username and password.
After establishing a connection, select a local directory to save your backups to (left pane) and then select all the files on your host (right pane).
Transfer the files from your host to your local directory. In FileZilla, right-click on the selected files and select “Download” or simply drag the selected files over from the right pane, to the left pane.
After your host files have completed downloading, you can compress the files using your favorite compression program, like 7-Zip. This step is not necessary, but it can save you lots of disk space if you store several backups or more.
Log in to phpMyAdmin. phpMyAdmin is a Web interface for mySQL administration. If you don’t know how to get to phpMyAdmin, your host should be able to direct you. For GoDaddy, go to your Hosting Dashboard, Databases, then mySQL
The left column of phpMyAdmin lists one or more databases. Select your WordPress database from the list.
In the Export tab:
A. Click “Select All”
B. Select “SQL”
C. Check the boxes next to, “Add DROP TABLE / VIEW / PROCEDURE / FUNCTION”, “Add IF NOT EXISTS”, “Add AUTO_INCREMENT value” and “Enclose table and field names with backquotes”
D. Check the box next to “Complete inserts”
E. Check the box next to “Save file as”
F. Click the “Go” button to start the export.
When prompted, select a location to save the .sql file on your local computer and save it.
Caution: Do not poke around other areas of phpMyAdmin and make changes unless you know what you’re doing. Changes made to your database in phpMyAdmin cannot be undone.
Congratulations–you’ve successfully backed your WordPress site! The next time you need to upgrade WordPress, you’ll know how to quickly back it up before upgrading. Consider burning your backups onto a CD or DVD as well, for safe keeping.
Source: CNet News