Welcome to New Orleans, Jazz Fest visitors; newbies and veterans alike. You're going to have a great time at the festival and the many after-fest events that happen around the city each day! The Fairgrounds are great but you're likely staying at least a couple miles away from there as the area around the festival contains neighborhoods, not hotels. With that in mind, here's a quick rundown on getting to and from the festival each day:
SHUTTLE
The "Jazz Fest Express" is the official festival shuttle and the only one that takes you inside the gates. The Jazz Fest Express has pickup/drop-off points at the following locations:
Steamboat Natchez dock by the Missisippi River
Sheraton Hotel at 500 Canal St.
City Park (price includes parking)
To purchase Jazz Fest admission and Express shuttle tickets by phone, call 504-569-1401 or 800-233-2628 through 4pm on April 23 (for the first weekend) and through 4pm on April 29 (for the 2nd weekend). Advance tickets also available here: http://www.graylineneworleans.com/jazz-fest-express.html.
Shuttle & Festival admission tickets will be on sale at the Shuttle Departure Locations listed below on the days of the Festival beginning at 9:30am. All shuttles begin operating at 10:30am (gates open at 11:00am) and will operate until all patrons have been transported from the Fairgrounds.
BICYCLE/WALKING
This isn't going to be at the top of everyone's list, but it's the top of mine as long as your accommodations are within a few miles of the Fairgrounds. If you're staying in the French Quarter, it's about 3 miles to the festival. Biking or walking will get you super close to the festival, there is always bike parking available, and you don't have to pay for it. It's easier to navigate the inevitable traffic jams that happen near the Fairgrounds when on a bike (wave at the cars as you whizz by them), and biking makes for a much faster escape at the end of the day when you're sunburnt, tired, and ready to get out of there quickly. There are many bike rental places in the French Quarter.
That all said, if you're not an experienced city bicyclist, you probably shouldn't start now. There are rules of the road (yes, road, not sidewalk) for bikes and learning them during a busy time isn't the right way to start.
STREETCAR
The Canal Street Streetcar line runs from the Mississippi River up Canal Street, with one spoke that terminates at Beauregard Circle, at the edge of City Park. City Park is walking distance to the Fairgrounds (just over half a mile). The Streetcar isn't the fastest option, but you'll feel very New Orleans on it. On the way there, get on the streetcar that's heading to "City Park/Museum." On the way back, they're all going the same way, to the Central Business District/French Quarter.
BUS
The Regional Transit Authority has extra buses running to and from the Fairgrounds during Jazz Fest. Buses run slightly closer to the festival than the streetcars do so if you can't or don't want to walk the 0.7 miles to the streetcar stop, the bus is another option. The best bus route depends, of course, on where you're staying. Most hotels are in the French Quarter and Central Business District. The #91 bus starts in the Garden District near the corner of Jackson and Tchoupitoulas and runs past the French Quarter on Canal and Rampart. On the way back, you can take the #91 that comes back down Esplanade and Rampart, or #48 which comes down Canal.
TAXI
Taxi drivers are hopping during the festival weekends and the week in between. Be patient, fill empty seats in taxis whenever possible, and know that, no matter what happens, you'll eventually get to where you're going. Also know that after the festival is over each day, here are two taxi stands outside the gates which are the only places taxis are allowed to pick up or drop off at that time.
DRIVING
There is street parking in the neighborhoods around the festival but it will be difficult to find and if you're not sure the spot is legal, it's probably not and you'll definitely get a ticket or get towed (or both). You must be parked at least 30 feet away from corners. A safer bet is to pay any of the nearby churches, schools, and private residents that sell parking on their property during the fest to raise some extra funds.
Locals, what did I forget? Let 'em know in the comments below, please!