This article is the culmination of several threads you should be able to find on the forums in the FAQ and General Discussion sections.

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What is Airsoft?

Airsoft generally has different definitions based on what organization you participate with. However, there are the following overall general concepts:

1.) Airsoft is a sport involving weapons and tactical interactions of participants with those weapons, much like paintball.
2.) Airsoft weapons are generally replicas of real-steel firearms, allowing a more effective military simulation.
3.) The weapons usually shoot 6mm plastic pellets at velocities between 100fps and 500fps, a safe speed that minimizes injuries

ASIL-specific definitions of Airsoft:

4.) Airsoft is based on the honor system; that is, when you are hit, there is no referee to verify the hit nor a mark that you would find in paintball. You are responsible for calling your hits.
5.) Airsoft brings together tactically-minded individuals in participation in squad-based tactics. Airsoft allows players to go beyond 'speedball' and participate in more realistic firefight scenarios.

For a more concise history, explanation, and overview of Airsoft, please check out http://en.wikipedia.org/wiki/Airsoft (note, this is a wikipedia, which means it is user-updated, and therefore can be less-than-completely-accurate).

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What do I need to play Airsoft effectively?

That is an absolutely loaded question, which makes me wonder why I asked it, but i'll try to answer it anyway:

Weapon(s):
Primary:An AEG is recommended as your primary weapon. It has full auto capabilities in most circumstances.
Secondary: Most players carry a back-up for close situations or when a magazine runs out in a quick situation.
Magazines: As of now, ASIL does not regulate magazine types, but it's recommended that somewhere on your person you have at least 500 rounds. I generally carry closer to 1,000 in the form of 700 or so in magazines and 300 in speedloaders.

Clothing:
Uniforms: BDUs are required for playing at ASIL events. Jeans are not allowed unless for a very specific role, nor are non-BDU tops. I recommend for starters that you get cheap camo uniforms at a military surplus store. Right now, due to military changes, Woodland camo and DCU (Desert Combat Uniform) patterns are cheap cheap cheap!
Footwear: Wear something comfortable but fitting to your role. Hiking boots are acceptable, but tennis shoes are pushing it. Combat boots are recommended, but don't be stingy on footwear, you will be moving about 6-8 hours during an event.
Headwear: Wear something comfortable but in tune with your uniform. Bandanas are a good way to go in hot weather (or no hats) and typical patrol caps/boonies are a good way to go year round. Carry with you warmer hats in colder weather, and be ready to protect your ears when it gets cold.
Under it all: I don't care what kinds of skivvies you wear, but keep yourself warm and dry. UnderArmour brand undergarments are a good way to go for the legs and torso, as is any wicking type clothing. That should be your lowest layer, followed by whatever clothing you need to keep warm.

Gear:
Hydration: First and foremost, figure out how you can carry at least 2 Liters of water on the field with you. Canteens and Camelbaks are the best ways, water bottles are good too.
Vest: Good Load-Bearing equipment can get you far. Military surplus LBVs are only 10-20 bucks and carry all your mags, radio, etc.
Pouches: If not integrated into your vest, get a good number of pouches that allow you to carry everything on your vest comfortably. Weight should be distributed well and you should not feel restricted in any way when wearing your LBE.
Weapon retention: You don't want to be carrying your AEG all day without some sort of support. Most players get a 1- or 3-point sling to use on the AEG and a holster for their sidearm.
Radio: You are required to have an FRS radio with you and enough batteries to keep the radio operating for the length of the event. We don't want anyone getting lost without a radio, so bring it. No arguments.

Safety:
Goggles: You are REQUIRED to wear ANSI rated and sealed goggles to events. There is no argument, this is a LEGAL issue and you will NOT be allowed to play without these goggles. They protect your eyes, so get good goggles. ESS is a good starter brand, and most paintball goggles fit the bill for what you need.
Barrel covers: You need something to cover your barrel with to prevent the discharge of your weapon when you're around players without goggles on. Again, no argument. Weapon handling skills are a requirement to play at any ASIL event.
First Aid: This is not required, but I recommend you carry basic first aid with you in the event you injure yourself and you're alone. I also suggest that you take basic CPR courses for the unlikely event of a medical emergency.