Is it possible to run a dedicated server from a webserver? If so, how can I do this?

i think so, just install standard soldat on it if it is a windows server or the dedicated linux server version on it if it is a linux server

No it is not, and will probably not be allowed from your webhost.

A webserver is actually ON a dedicated server, A webserver is simply a HTTP daemon like Apache or similiar. So if you have a server with SSH access yes you can install soldat.

The only way it would be possible from your hosting account would be if you have SSH/Telnet to run the commands.

or vnc

We own our own server with SSH capabilities, so how would I go about doing this?

Copy the link in your browser, then log in to your server (not root) then hit:

wget linkhere

(I'm kinda lazy and I'm not going to paste the link for you)

Unzip it with: unzip soldatdeblablabla

Then edit soldat.ini, then I recommend my software (Soldat Guardian) and run it with ./soldatguardian, then try to connect to see if it works, if it does sit back and play!

er, but be warned that doing this is a good way to get your account dropped from your webhost.

well if he OWNES his own server as in its in his house that would be abit unlikly