Heero Yuy = 1. He comes from colony #1 and his name means, roughly translated, "the one and only". He also pilots Gundam 01 (Wing & Wing Zero).

Duo Maxwell = 2. Originates from colony #2, unsurprisingly, and his name means "two" (which y'all knew, of course). He pilots Gundam 02 (Deathscythe, Deathscythe Hell, Deathscuthe Hell Custom).

Trowa Barton = 3. Comes from colony #3, his name looks like the French word for "three" ("trois") and he pilots Gundam 03 (Heavyarms, whose main purpose seems to be running out of bullets).

Quatre Raberba Winner = 4. Comes from colony #4, his name is French for "four", and he pilots Gundam 04 (Sandrock).

Wufei Chang = 5. He comes from colony #5, and "wu" means "five" in Chinese. I bet you're not surprised to hear he pilots Gundam 05 (Shenlong or Nataku).

Zechs Merquise a.k.a. Milliardo Peacecraft = 6, because "zechs" is German for "six".

Lucrezia Noin = 9. "Noin" looks vaguely like the English "nine", and it's also the phonetic spelling of "neun", which is German for "nine".

Lady Une = 11. This puzzled me for a while, until someone at the 1x2 fan community on LJ pointed out that there are two Lady Unes, hence the double "1". Clever, no?

Treize Khushrenada = 13. "Treize" is French for "thirteen".

Then there are the numberless characters:

Relena Dorlian/Peacecraft = R.

Sally Po = S.

Dorothy Catalonia = D.

Hilde Schbeiker = H. (And yes, that's how you spell it.)

Meiran Long = M. (She was Wufei's wife.)

So if you see a story headed by, for instance, 1x2 and 3x4, it means the pairings in that story are Heero/Duo and Quatre/Trowa. These pairings, alongside 13x6, are the so-called "traditional" pairings, meaning that they're the most common ones. The small "x" denotes a physical relationship. If, instead of an "x" there's a "+", it means the relationship isn't physical, but kissing might be involved. The "x" stories are called "yaoi" ("yuri" if the characters are female) and the "+" stories are termed "shounen ai" ("shoujo ai" if the characters are female).

The other thing you need to know that the character on the left of the "x" or "+" is the dominant partner, the so-called "seme". So 1x2 means that Heero is the top and Duo the bottom ("uke"), whereas 2x1 means that the roles are reversed. 1x2x1 means that they're equals or that they're switching roles in the story.

Yaoi stories vastly out-number het or gen stories. TPTB of GW have stated that GW is not (repeat not) about romance, not even the Heero/Relena (denoted as 1xR) kind. They deliberately left it open as to attract the huge yaoi fanbase. There's as much support for 1x2x1 as there is for 1xRx1, so the fans are free to pair up Heero with either Duo or Relena. I do like Relena, but in my mind, Heero is better suited with someone who's gone through the war the same way he did, someone who knows what it was like, someone who knows how it feels living your life killing in order to not get killed yourself.

Specific GW-related terms:
RFO: Relena Finds Out. Self-explanatory; Relena finds out Heero has a relationship with someone who is not her, obviously, usually Duo.
TWT: Timeline, What Timeline? Indicates a story doesn't take place within the series/Episode Zero/Eternal Waltz timeline of GW. For instance, post-EW stories. TWT can also mean that the time in which a story is set isn't important to the story itself -- such as random "safehouse" fics.
Canon pairings: (also called "traditional pairings") This is a bit of a misleading term, since there are no official pairings within the GW canon universe (Treize/Une or Zechs/Noin is about to close as canon you can get and you could even argue against those). In fanfiction, "canon pairings" means the "traditional" pairings of 1x2 and 3x4 with some 5x6 or 5xS (or 5x13 -- yes, Wufei gets around) thrown in for good measure. These aren't canon pairings, but they are the most common ones.

Other important yaoi terms are:
Lemon: stories with graphic/explicit content
Lime: stories with not-so-graphic/explicit content
Citrus: implies some form of graphic content
shounen/shoujo ai: respectively boy/girl-love. Non-explicit.

GW writers are wont to use a lot of Japanese in their stories (Heero is Japanese, after all, even if he doesn't really look it, IMO. Blue eyes?). Here are a few of the most commonly used words/phrases:

baka: idiot, stupid person (applied, in the world of fanfiction, most often to Duo)
bishoujo/bishounen: beautiful girl/boy
gomen: I'm sorry or excuse me
hai: yes
itai: exclamation of pain, "ouch!"
nani: what
omae (w)o korosu: "I will kill you" (tm Heero)
onna: woman (used mostly by Wufei in a derogatory way)
Shinigami: God of Death. Duo nicknamed himself this way, and it's way overused, FWIW.

There's, of course, lots more to learn, but the best way to learn is to surf some webpages, join some mailinglists, read a lot of fic, and educate yourself :). Come on in; the water's nice.