Hobbes has described the game play fairly well, but no one said what you need to play. The most important things may very well be the Players Handbook, and a set of dice.
The dice are of seven different kinds, each with a different number of sides. Ex: d4 has 4 sides. The dice types used are: d4; d6; d8; d10; d12; a ten sided die where the numbers are in the 10s values; and the die you use the most of all of them, a d20. They are often sold together as a set, but I have always loved finding individual dice that suit my taste.
The player guide helps you choose a character’s race, class and defining characteristics.
Two other books that are pretty much a necessity, are the Dungeon Masters Guide, and a Monster manual. The DM guide is obviously a guide to assist the Dungeon Master in making the game fun. A monster manual has a large variety of npcs (Non-Player Characters) for your adventurers to encounter, whether they be friend or foe (mostly foe). You can usually find places online to view the books for free, but having one with you at the table is way more useful.
You’ll also require something to represent the characters. They have figurines for this, but anything will work. I have often used chap-stick that looks like a mini Mountain Dew can as mine. A good cheap resource to show all the enemies is some half marbles.
Lastly is a play mat. You can create one of your own, or buy one, but it is basically a large rectangular surface that has a grid covering it. If you make it yourself, the squares on the grid are about 1 inch wide and tall. A big piece of paper that you can roll up for later works well.
Remember, the books are just guidelines, you can mold it into whatever you want.
The game is TONS of fun, and you’ll have many times where you’ll laugh till it hurts.
(Or bleeds in some unfortunate cases) One last thing, you should have at least a few people to play, one as the DM, and 4ish-8ish as the party of adventurers.
Sorry that was so long, wish you luck in having fun with it if you want to try it out!