Stylin'
"Never the twain shall meet"
Rudyard Kipling (1892)
Homophones are words that are spelled differently but are pronounced identically. The homophonetic world is a place where monsters lie in wait for the intrepid EFL student. The most used and confused sound-a-likes are: there, their, and they're; its and it's, your and you're; and to, too, and two. The first order of business is to review one's contractions. A contraction happens when an apostrophe stands in for a few letters who have stepped out for çay, as in "they're" (they are), "it's" (it is), and "you're" (you are).
Unless you are in creative writing class, keep is simple; do not use a contraction. "Their" is third person plural possessive, and if your grammar-check is like mine, Word has auto-changed each sentence I've tried to start with "they're" or "their" to "there." Computers are not smarter than people, but they are useful tools.
So, let's get to the fun homophones, a group that even has its own Facebook page, "to, two, and too": http://www.facebook.com/pages/To-Too-and-Two-mean-3-different-things-Really/321306991993?v=wall.
"Two" indicates a numeral, one thing plus another. In English, often we can look to cognate languages for our roots. ("Cognate" comes from Latin "cognatus, -a, -um," an adjective meaning "born together"; in English, cognate means "descended from" or "origin.") "Two" comes from Old English, specifically via Frisian, a Germanic language group from the land area between modern Denmark and Holland. "Two" originated in the feminine numeral twá, or so says the OED. The masculine numeral for 5 minus 3 was twéen, which survives in Modern English in the word twain, meaning in two parts, kind of like the second part of between, indicating two (for discussing interactions concerning three or more actors, use the word "among"). Wait, twain looks familiar. Isn't that the name of a rather good American author, first name Mark? Well yes and no. Mark Twain was the nom de plume of Samuel Clemens. Clemens used nautical language when he was a young riverboat hand. "To mark" as in to measure, indicate, or notice, comes to what we call English variously from the Old Frisian, Middle Dutch, Old Saxon, Old High German, Old Swedish, and yes, our favorite, Old Icelandic. So "Mark Twain," in 19th-century American nautical, means the knot on a depth-gauge rope indicating two fathoms (Old High German again meaning 2 x 6 feet, or 12 feet, or 3.6576 meters) deep. So, if you need a penname, consider calling yourself "3.6576." It's better than "the artist formerly known as…"
English is one of the very few languages in which infinitives are expressed in two words. An infinitive form of the verb is the pure meaning of the verb. Think of a verb standing alone in a club waiting for a subject to come by and offer to buy it a drink. Our homophone "to" is part of the English infinitive form: as in "to buy." "To" also indicates direction, the opposite of from, as in "go to class." If you are a grammar nut, "to" has a long and complicated history in all of the language streams and spates that tumbled into the raging torrent of English. I will direct you to the OED for further study.
"Too," at least is a somewhat straightforward (for protean and complex English) adverb, a synonym of also, but it also means excess: "To learn, the two of you should go to class too; that's not asking too much."