This might be text book stuff to some, but not to me, so perhaps someone could explain this to me:

A friend works for a big bank, but in one of their computer centres,  and he wants to get a PC for home, which he wants to be able to use on the bank's own network, to enable him to 'work from home'.  How would he achieve this?

This does kind of beg the question, "How did he get a job in their datacentre, when he can't figure out a Homeworking connection?"

I would imagine that if he's of sufficient status within the organisation, they'll provide him with a secure home connection as a matter of course.  If he's not, then he should put forward a strong case supporting his request and present this through his departmental manager, who might then take the steps necessary to put it on track for consideration by the bank's Security / Network / Procurement departments (budget permitting).

I would be very surprised if they allowed him to use a machine he's bought himself to interface with the bank's systems and there is a major security issue here, Simon!  How well do you know this guy?

An easy way to do it would be to use an FTP server and for whoever had the server to allow access to which people they wanted to be able to log on with a password to the parts of the server that they needed access to.
A friend of mine has set one up and allowed me full access when I log on to all the files he has on it and hes restricted a specific folder for another friend to be able to get files etc. from me if I upload stuff to his site  

Thanks, Adept - that sounds like the sort of thing that would suit.  He should be able to get ADSL from home.