What is the best way to allow a member to delete their account if they wish to not be a member of our community? Should I simply have them click a delete button on the site? What other measures should I use?
One factor to think about is that of the "malicious" or "mischievious" friend. Or, simply, that people change their minds.
I suggest that you give users a way to deactivate their account, but with an escape hatch of some kind - an emailed confirmation link perhaps, or "account deletion will occur in 30 days unless you change your mind".
Taking @Bevan's idea a bit further:
Have a "deactivate account" link which sends an e-mail to the registered e-mail address. That says something along the lines of:
I'm not sure you need to do all of this, but you get the idea.
By sending the e-mail to the registered address you guard against malicious or mischievous attempts to delete the account (in much the same way as you should treat any change to the account details). The e-mail gives the user confidence they can back out and also recover their account in the future if they change their mind.
However, if deletion is a unrecoverable option you could warn them instead:
Again, giving the user another chance to change their mind.