You have to copy the web and web-inf folder to the web server. You also have to set up the IIS or Apache server using some configuration files, which are provided in the documentation section. You also need to have a mendix business server running in order to interpret the model. You can run this as a windows service if you wish. I have only set up web servers twice and it is a bit tricky the first time! So good luck and i hope this basic information helps.
It is not completely clear to me what kind of servers you refer to with 'publicly hosted', so note that you cannot use an arbitrary LAMP setup (linux, apache, mysql, php; most cheap website host servers), but need Java as well. See this thread for more details. In practice, you need to have full access (root permissions) on the server to install mendix.