How to sign a transaction using only an offline computer?
You're correct that the offline node needs to how to claim its funds, so it can't be totally isolated. 

Currently, the most mature offline wallet solution is through a client called Bitcoin Armory. Here's what your workflow looks like with offline wallets:


  Online node creates transaction -> USB key -> Offline computer signs transaction -> USB key -> Online node broadcasts transaction


You can use Windows, Linux, or Mac for your offline wallet, but I'd recommend Linux, as it's difficult to disable AutoRun/AutoPlay on Windows.

Download:


Windows/Linux
Mac - Beta


This page explains offline transactions in greater detail.