How can I make a sliding menu like (as an example) Sparrow’s main email menu?
In the case of Sparrow:
It’s a column of buttons that essentially slide to reveal a NSScrollView (with custom NSTableView?) with various folders inside (inbox, sent, etc). Clicking on a different account causes that account to slide up to the top and reveals the various folders inside.
How could I go about doing a menu similar to this?

There is some fairly cool Apple sample code here to deal with table views and animation (uses stuff that is generally only available as of Mac OS X 10.7 however):
https://developer.apple.com/library/mac/#samplecode/AnimatedTableView/Listings/ATPopupWindow_m.html%23//apple_ref/doc/uid/DTS40008863-ATPopupWindow_m-DontLinkElementID_26
Also, for basic window resize animation you can use the
setFrame:display:animate:method ofNSWindow.