Depending on what server setup you have (operating system, http server & control panel – if you have one), the main way to go would be to have separate DNS zones for each domain (with an A record for the domain name, then MX records, NS if you want the nameservers to be linked to that specific domain, reverse lookup and other stuff), then have a virtual host for each domain, having the DocumentRoot point to the specific installation folder.
For the classical LAMP stack, the virtual hosts would most likely look something like (a very basic setup – the minimum number of directives needed to accomplish this task):
<VirtualHost *:80>
ServerName foo.com
DocumentRoot /public_html
<Directory /public_html>
Options Indexes MultiViews FollowSymLinks
AllowOverride All
Order allow,deny
Allow from all
</Directory>
</VirtualHost>
<VirtualHost *:80>
ServerName bar.com
DocumentRoot /public_html/wp_subproject1
<Directory /public_html/wp_subproject1>
Options Indexes MultiViews FollowSymLinks
AllowOverride All
Order allow,deny
Allow from all
</Directory>
</VirtualHost>
<VirtualHost *:80>
ServerName anything.com
DocumentRoot /public_html/wp_subproject2
<Directory /public_html/wp_subproject2>
Options Indexes MultiViews FollowSymLinks
AllowOverride All
Order allow,deny
Allow from all
</Directory>
</VirtualHost>
As far as keeping the user from actually knowing that your domains sit on the same server, I believe you want them to see each website on its’ own, which is what this setup does. In terms of actually hiding this fact from advanced users, things get more complicated since a simple ping on each one of the domains would reveal that they are on the same IP (so yould need to hide this – have 3 separate IPs and do some fancy magic to route calls to each of the domains through one of the IPs).