The first part is a glossary of general terms that get thrown around in any fandom; the second part is a glossary of slash pairing terms in the Newsies fandom.

Alternate Universe — An AU (for short) is a fic that takes place outside of the traditional canon setting, but uses the canon characters. These show up most frequently in the Newsies fandom as stories set in a modern day school, but they can really be set almost anywhere or anywhen.

Beta reader — Someone who reads through your story before you post it, lets you know where you have mistakes (which you should then fix,) and gives you advice for improving your story in general.

Canon — Something that's canon is something established by the movie. As a writer, you don't have to like what's canon, but you ought to respect it. If you write outside it, try to find some way to explain why; if you don't do that, at least label it as alternate universe.
For example: Sarah Jacobs is probably the most hated character in the fandom. But she still exists. Even if you're writing slash about Jack and, well, anyone, you should still mention her. Did they break up? Did she die? Did he dump her? Respecting canon makes your fic fit into the Newsies universe, which ought to be one key goal while you're writing.

Fanon — Obviously, this is somewhat similar to canon. However, these things aren't established by the movie, they're established by the fans. Unlike canon, these things don't have to be respected, because they aren't part of the Newsies universe.
An example of fanon is Racetrack's real name. The movie tells us he's Racetrack Higgins, and fanon usually refers to him as Anthony Higgins. Not every fic writer uses that name, but it's an almost sure bet that if you run across an Anthony, it's him. Fanon can be used or ignored as the writer chooses.

Mary Sue — A self-insert gone terribly wrong. This will be expanded on in a later section. (Her male counterpart is Gary Stu.)

Muse — Occasionally authors adopt muses (or, in some cases, the other way around). These are characters who inspire you to keep writing, usually the main character in your stories. Occasionally, authors refer to their muses as living in the back of their heads, yelling at them, and other things—and the muse version of a character can be a bit different than the canon version.
I, for one, have a Blink!muse (that's how it's punctuated—don't ask me, I can't explain why) in my head. I keep him in a cage so he doesn't get out of control, as he tends to be whiny and demanding. He's also sleeps around a lot and isn't terribly bright. So it goes.

OC, OFC, OMC — Original Character, Original Female Character and Original Male Character respectively. These are just what they sound like, a character (male or female) that the author created, who isn't a part of the canon universe.

OTP — This stands for One True Pair, and is how people refer to their absolute favorite couple in the fandom.

OT3 — Similar to OTP, this is One True Threesome.

PWP — This stands for Plot? What plot? And refers to a story which is nothing but an excuse for characters to get it on. These usually are slash stories, but not always. Lemon is also a fic with strong sexual content.

Self-Insert — A specific kind of OC, also sometimes called an avatar, which represents the author of the story.

Slash — Slash is a specific kind of romance between two male characters, who generally aren't presented as gay in the canon. (Romance between two girls is usually called femmeslash. And, incidentally, in anime fandoms, slash is referred to as yaoi and femmeslash as yuri.)

Songfic — A songfic is a story that makes uses of song lyrics throughout. Generally, the lyrics reflect what's going on in the story.

There's a far more extensive list of terms here if you're looking for something that isn't listed here.

Pairing glossary, the most commonly used pairing names:

Blinktrack - Blink/Race

Blush - Blink/Mush

Blushtrack - Blink/Mush/Race

Decs - Specs/Dutchy

Ducs - Specs/Dutchy

Dutchlets - Dutchy/Bumlets

Jacktrack - Jack/Race

Javid - Jack/David

Javot - Jack/David/Spot

Snitey - Snitch/Itey

Snittery - Snitch/Skittery

Spack (Spackle) - Spot/Jack

Spavid - Spot/David

Sprace - Spot/Race

Spetchy - Specs/Dutchy

Splinktrack - Spot/Blink/Race

Sputchy - Specs/Dutchy

Sweater - Swifty/Pie Eater

Swiftlets - Swifty/Bumlets

Something confusing, or are you wondering about a word that's not listed here? Ask me.