The installation notes at
http://code.google.com/p/webiopi/wiki/INSTALL give details of your options for starting the service on demand or at system startup.
This only gets the webiopi web page visible to your local network. To access it from the global internet you will have to research how to configure Port Forwarding on your internet access router. The details of this are specific to your model of router and are not directly related to the RPi, which itself needs no change to be used in this way.
[EDIT] Port Forwarding is also the key to your parallel thread about this. It's just about your BT router, no change needed at work (provided they don't have network access policies that restrict what you are trying to do) or on the RPi itself.
How To Ask Questions The Smart Way: http://www.catb.org/~esr/faqs/smart-questions.html
How to Report Bugs Effectively: http://www.chiark.greenend.org.uk/~sgtatham/bugs.html