It seems that code completion (e.g. intellisense) is a hit or miss thing within Eclipse/ForceIDE plugin.
Is there a page or something that spells out how and when it actually works?
Try right clicking on the line you're working on or a blank line. You'll then get "content assist". Is that what you're referring to? Just like when working from within SF UI, it's very limited. You basically need to know the code and what you plan to write.
Once you start typing something, it sometimes will present a pop-up, particularly when you type a
. and present you with context options that you can select. More often than not, I personally find the feature to be a nuisance. I've never searched the SF Help (there's a specific one for the IDE in the drop down) to see how it's supposed to work.