One of the great things about New York City is all of the free options for entertainment, specifically seeing the magic of some of your favorite TV shows live, in person.  For me, that list of shows includes Jimmy Fallon and Comedy Central's two "news" gems - The Daily Show and The Colbert Report.

Jimmy Fallon
This applies to the current Late Night with Jimmy Fallon show, but I can't imagine it changing much when he starts his engagement as the new host of The Tonight Show in February 2014.  Instructions for tickets are on this website.   I had luck trying about 6 weeks in advance first thing, as soon as the phone lines open up.  If the dates were not available yet, I would just try back every day thereafter.  The day of the show, you will have to pick up your tickets in advance of the show at the NBC Studio Experience store in Rockafeller Center.  I would suggest getting there by 1pm, earlier if the guests are very popular.  You will receive a ticket with a number and a wristband.  Come back to Rockafeller Center at the time they indicate.  You will then line up and be escorted to the studio by NBC pages. The taping I saw, Jimmy was spot on and did not require any edits.  Such a talent and such a fun show!

The Daily Show and Colbert Report
The first thing you will need to do to get tickets is ignore the ticketing websites.  You will need to have or create a Twitter account at least two months in advance of the dates you desire, follow @Spiffomatic64, and prepare to monitor your feed for the release announcement of your date.
For The Daily Show, once you have a ticket reservation, you still are not guaranteed a seat.  There is a two stage ticketing process the day of the show.  First, you must stand in line to get your ticket.  The tickets are officially given out at 2:30, but the line can start as early as 12:30-1pm.  Once you get your ticket with a number, you are set loose for two hours and told to return to the line, in numerical order, at 4:30.

Back in line, corralled by your ticket numbers, you get the security speech and the bathroom speech. Definitely take advantage of the bathroom because you won't be able to go once you're in the studio. You are ushered into the studio in order, but your number does not necessarily mean you will get the best seats.  By 5:30-5:45pm everyone should be in their seats, at which point you are allowed to take photos of the studio.  The warm-up comic comes out around 6:00pm, followed by Jon Stewart for a short Q&A. Taping starts at 6:30pm and will end as early as 7:00pm, if no retapings are required.

For Colbert Report, the ticketing process is a little easier.  There is just one line, thankfully.  We had luck arriving at 4pm, but you also should consider the time of year and the weather conditions.  At about 4:30pm, studio assistants came out and processed the line, checking for reservations and giving out numbered tickets.  You are then asked to have at least one person in your party stand in line at all times, but you can switch off and go get food.  

Around 6:00pm, we are ushered through security into a waiting room with two TVs playing "best of" Colbert clips.  Finally, they call everyone's tickets by number, and you are directed to your seats.  Again, the number does not necessarily mean your seats are good.  A warm-up comic comes on to ramp up the energy, then Stephen Colbert comes out for a quick Q&A before starting the show.  The taping was really fun, especially seeing Colbert cracking up while the hilarious video packages were playing, yet still getting it together just seconds before the camera is back on him.  Now that's comedic talent!