There are four different ways of backing up your WordPress install that I know of. Two of the four are render the same results with different options along the way. One of the other backup methods safeguards a whole different set of information than the first two. And the last one, though built right into WordPress, seems to be broken and unreliable.
The first two ways back up all of your websites data. This includes all of the posts, comments, categories and anything else you can think of as content except for your photos and other uploaded media. The easy way to do this backup is to install the WP-DB-Backup plugin using the plugin manager in WordPress. Once that is installed you choose Backup from the Tools menu to set the option of the various data you want stored and where you want it stored to.
The second way to perform this first type of backup is to use a program like phpMyAdmin and do a database dump. This gives you more control over the exact data you want backed up, but is certainly more complicated than the average user will want to go through.
While those two can back up your data, you will still want to do a backup of the structure and media for your website. To do this, you need to log into your webhost account using an FTP program and copy the wp-content folder to your local computer. This will copy back all of your themes, plugins and media. This is important because any changes you make to the theme you are using will be lost if you need to restore your website and simply download the theme again. By uploading the wp-content folder that you copied to your local computer, you will have a full backup. The wp-content folder also contains all of the pictures, videos and audio files you may have uploaded to your blog
The fourth type of backup is built in to WordPress, but seems to be broken for me. Enough so that I won’t trust it to give me a full WordPress backup. It is a feature called Export that you can find in the Tools menu on your WordPress dashboard. My experience with it did not export my complete site. It should be essentially the same as one of the first two types of backups mentioned above. Since the WP-DB-Backup plugin works so well, there is no reason to risk the Export feature working correctly when you can do a full backup using the plugin.
It is important to do at least 2 of these backups so that you get all of your data and all of your media stored in a safe place.