You can host your own personal webpage at Blinkenshell. To do this, put any files you want to be accessible via HTTP in the directory public_html in your home directory. The URL to your webpage will be http://username.blinkenshell.org/
If you have a file named index.html in your public_html directory that file will be used as the index page when someone browses to your site without requesting a specific file (i.e. http://username.blinkenshell.org/). If you do not have an index file a directory listing of all the files in your public_html will be shown instead.
You can use Apache .htaccess-files to customize the behaviour of your webpage. Apache documentation on htaccess.
Logs from apache are written to ~/logs/access.log (normal traffic) and ~/logs/error.log (errors). These files are not writeable by your user and you can not delete or truncate them. This is because the logs are used for measuring traffic to your website.
You can use PHP and CGI scripts to create dynamic webpages. CGI and PHP scripts are executed with mod_fcgi and suexec, which will make all scripts execute with your user id instead of the Apache user.
For information on how to use MySQL, see: Info/MySQL.