You can also use Google Docs for this. Simply create a form and make it public available.
An easy way how to do this is described here:
http://www.ehow.com/how_4615530_survey-using-google-documents-free.html
or shown here: http://www.youtube.com/watch?v=H-lNffCvY3A
One tool to solve this task is Limesurvey. It is open source and written in PHP.
The survey data is saved into a MySQL-database.
*) To install Limesurvey on the webspace provided it is sufficient to unpack it into the appropriate folder and run the setup script.
*) Then you have to create a MySQL-database, the TU provides a web interface for that.
*) The username, password for the Database have to written into the configuration file of Limesurvey. The easiest way for that is to log in via ssh and use a text editor like nano.
*) Limesurvey also needs to keep track of user sessions. Usually it creates temporary files for that but the permissions on the server don't allow that. Therefore you have to change this so Limesurvey saves the session data into the database.
You can create your survey now.