Fetch Time Machine backup information onto *another* computer

My wife's MBP went south. I will need to fetch her Time Machine backup information onto a computer not hers, obviously—either a new laptop or, for now, mine. Would someone please have the kindness to point me to the URL of Apple's (or someone else's) instructions on how to access those folders? Thing is, all I REALLY need is Documents and Downloads folders, and a quick glance at Desktop in case she left any stragglers there.