It is not "He gets his just desserts"

The noun "desert" (accent on the first syllable) is generally used to refer to an arid, barren expanse of land; the noun "dessert" (accent on the second syllable) is a sweet course or dish usually served at the end of a meal. However, the word "desert" -- when spelled like the former but pronounced like the latter -- also refers to a deserved reward or punishment. Therefore, someone who does wrong and is punished in a suitable manner has received his "just deserts."

Many people, unfamiliar with the "reward or punishment" meaning of the word "desert," mistakenly assume that the phrase "just deserts" is properly spelled "just desserts" because of its pronunciation. (The usual reasoning is that a dessert is a type of reward one is given at the end of a meal, so someone who receives suitable rewards or punishments for his actions has gotten his "just desserts.")

When one gets what one deserves, good or bad, one is getting one's "just deserts," accent on the second syllable but spelled like the arid, barren lands.

The animal was deserted on the desert and had it's dessert.

Here, courtesy of dictionary.com, is a nice history to go along with Adam's post:

<<Word History: When Shakespeare says in Sonnet 72, “Unless you would devise some virtuous lie,/To do more for me than mine own desert,” he is using the word desert in the sense of “worthiness; deserving,” a word perhaps most familiar to us in the plural, meaning “something that is deserved,” as in the phrase just deserts. This word goes back to the Latin word dservre, “to devote oneself to the service of,” which in Vulgar Latin came to mean “to merit by service.” Dservre is made up of d-, meaning “thoroughly,” and servre, “to serve.” Knowing this, we can distinguish this desert from desert, “a wasteland,” and desert, “to abandon,” both of which go back to Latin dserere, “to forsake, leave uninhabited,” which is made up of d-, expressing the notion of undoing, and the verb serere, “to link together.” We can also distinguish all three deserts from dessert, “a sweet course at the end of a meal,” which is from the French word desservir, “to clear the table.” Desservir is made up of des-, expressing the notion of reversal, and servir (from Latin servre), “to serve,” hence, “to unserve” or “to clear the table.”>>

Check out the following site (pay particular attention to the second and third last paragraphs).

http://www.snopes.com/language/notthink/deserts.htm

Also check out the following.
http://phrases.shu.ac.uk/meanings/213400.html
http://www.dictionary.cambridge.org/define.asp?key=43212&dict=CALD

Perhaps there is someone who would do well checking out the following too.
http://www.dictionary.cambridge.org/define.asp?key=60393&dict=CALD