I hate these words. I never know which one to use; and they both sound like feminine hygiene products that I didn't know I needed until an advertisement made me paranoid.
Discreet: an adjective meaning something or someone that avoids social embarrassment or distress by secretiveness.
Discrete: this adjective means distinct in form or concept. If the sentence involves data, this is probably the word.
Discrete data has values that are not infinitesimally close. So the number of Asbos given out in a patch in a year might be 2008: 4; 2009: 6; 2010; 3. These data are discrete, because you can't have 3.43245 Asbos. But if you have a list of heights of wrong-doers, that data set would read: 187.445cm; 134.567cm; 140.356cm; 189.001cm; 181.222cm. This is continuous data (and police are hunting high and low).
In the wild
He vomited discreetly into the wastepaper basket; wiped his mouth on a silk handkerchief, which he threw likewise into the same receptacle; and continued the interview.
Each volunteer group has a discrete budget for their own projects.
I am going to remember this because the avoiding social humiliation variety of discreet has double letters in it, just like embarrassment.