I must assume you already have an existing ISPConfig controlled server - either you are a client on one or you manage one. If you are a client then the critical thing to find out is whether you are in php safe mode or not. If you are and you cannot change it then I Moodle will not work. You either give up now or ask the administrator to change it for you. All they need to do is make sure than the php safe mode button is NOT checked.
Of course you also need to be able to create a MySQL database - ISPConfig has its own phpMyAdmin to make this easy to so. As long as the administrator has (a) installed this addition and (b) given you the ability to create a database (or has already created it for you).
Finally you also need ftp access.
Assuming that you have all this and the relevant usernames, passwords, etc then you are good to go. I'm doing the following from memory but if all the above works for you then it is just a standard Moodle install. (see the moodle.org site for details).
(1) Download the latest moodle install and ftp it to you home directory
(2) If all you want is a moodle install then you don't need your standard web directory (unless you intend to install moodle inside your site - e.g. mysite/moodle/ - in which case copy and expand the tar file inside the web directory.) so copy it just in case (cp -Rp web web.orig) then expand the tar file and rename it "web".
(3) Create a database (collation utf-8) in phpMyAdmin or use the one set up for you.
(4) Go up a level (so you see "web" as one of the directories listed along with cgi, etc) and create a directory for the moodle data (called, for example, "moodledata"!) It is important for security that this directory is out side the normal web directory. This should get the correct permissions but you may need to chmod it to 777 if there are problem - I run my own server and can go into the command line to do this. If you are a client of another administrator this will be a problem but, as I say, as long as apache can read and write to this directory all should be well. (It is this that is not allowed if you are restricted to safe mode).
(5) Copy the config-dist.php file to config.php
(6) Edit this file to give you the correct paths - site URL, site path (will probably be something like /var/www/web54/web/), data path (/var/www/web54/moodledata/) and the database details (dbname, host [ localhost]. username, passwd, prefix).
(7) Then access you site - the scripts will detect this as a new install and if all is well take you through the rest of the install and database creation. If there are settings missing or wrong it will put up quite good error messages.
Hope this helps and good luck!