Matt was kind enough to share some wisdom about late-night writing:
I took a Writing for The Daily Show class in NYC, Taught by a guy that writes for them: J.R. Havlan. It was a class to prepare us how to write a submission packet for the show. In a submission packet, they ask you to write 4 headline news stories, each containing five jokes. Pretty much you write the big headline for Monday, Tues, Wed, Thurs of a given week. Try to think of a clever puns for the title like they do. He suggested doing it on a week they have off as not to compete with their headlines. Basically we just kept writing headlines and he would give us feedback.
Here is the link to the class in NYC: http://www.thepit-nyc.com/classes.html#tds . They also do The Colbert Report and The Late Show classes.
Paul also had some insight:
As a former intern on a late night talk show, I got to spend the day with a couple of writers job shadowing them and picking their brains. The BIGGEST question I had was how they got staffed. The vast majority of the writers on the show I was at were either stand-ups or sketch/improv players. Many had quite a few other writing credits, but the younger ones (mid 20s) who were on their first staff writing jobs, had been writing promos for other networks and websites. They also had several freelance articles published in online and print humor magazines. They of course heard about an opening on the show from a friend who was a writer or writers' assistant and submitted a packet. Every talk show has its own packet and asks for different things. The network shows like Leno, Letterman and Conan are all going to want some solid monologue jokes. Letterman will ask for five or ten Top Ten lists, Conan's going to ask for more sketches. The Daily Show's not going to want monologue jokes because Jon doesn't do a monologue. They're going to want stories written in the same way Jon does them on the show (which means you should also include the OTS graphics which also better be funny) as well as a couple of host-reporter exchanges. For Colbert you're going to need stories as well as some show staples like Threatdown, Alpha Dog of the Week, Tip of the Hat/Wag of the Finger, etc. Oh yeah, and it all better be damn funny.
The good news is that you can probably call the writers' office and talk to a writers' assistant and they'll probably tell you what to include in the packet. They might only give this information to an agent, but the writers I talked to said you should be able to get it on your own. The bad news is that there are tons of people who desperately want these jobs and, just like sitcoms, it's hard to get your packet read by an EP without a recommendation from another writer, WA, or someone close to the EP. It's also not unusual for a WA to just throw away other packets they receive b/c they're also trying to get that sought after staff position, or so I'm told.
Don't think you can whip out a packet, send it into the show, and if you never hear back send them another. You have to take it very seriously and the whole thing better be hilarious. If they like your packet they may ask you to write another. They want to know that you can put out new material that's hilarious and current on the fly and that you didn't just send them a greatest hits collection of your best jokes. They'll also want to see other work which is where stand-up, published articles, or maybe your spec will help. The WA position can be a real stepping stone to late night staff writer if you can land it. Of course if my advice gets any readers a WA or staff writer position on a late night talk show I hope they'll let me know. I've already got a bunch of jokes about how (insert new President's name here) totally screwed up the country...and a Masturbating Bear sketch.
Oh, and one of the staff writers on the show I worked on also created a hit show for MTV. Sounds easy enough.