to diagram the white cat sleeps quietly
http://members.cox.net/teachro/
At this website, click on Diagramming. Then click on Nouns, Verbs, ... and then on Simple Subject and Predicate for the basic format. Then you'll need to go into Adjectives and then Adverbs to get help for those words.
Your sentence has these:
The - article, modifying cat
white - adjective modifying cat
cat - subject
sleeps - verb
quietly - adverb