Reddit mentions of Polyhedral Dice

You can download the rules for D&D here:

https://www.wizards.com/dnd/Article.aspx?x=dnd/basicrules

The Starter Set goes on sale in about a week, but some game stores are selling it early.

The Basic rules have all the info you need to play the game and make characters, while the starter set comes with an adventure, monsters and treasure.

The DM should buy the starter set, while the players will each need a set of dice, like these:

http://www.amazon.com/Dice-Festive-Chessex-Polyhedral/dp/B000RZLOM6

The starter set comes with dice. You can also share to start with, but it's a lot easier for everyone to have their own.

You'll also need paper and pencils. After that, you're good to go.

You don't mention what tabletop games you guys are familiar with. Not sure if that is RPGs or perhaps boardgames.

In a nutshell, here's how you play D&D:

1. DM describes the scene / environment.
   
   
2. Players describe what they want to do.
   
   
3. DM describes the results.
   
   What's a DM? It stands for "Dungeon Master" and is the person that serves as the referee. The DM adjudicates the game, has all the 'hidden' knowledge that the other players don't have, and controls / plays pretty much everything that the other players in the game don't. When a player wants to do something, the DM determines how difficult it is to do that thing and the results the occur if the player is successful or suffers a failure.
   
   Players generally play heroes that overcome obstacles, fight monsters, and interact with things in a fantasy setting. The DM comes up with the challenges that the players face, and the three-step process above is followed.
   
   Mechanically, the game has you define a character with several stats. These include six abilities: Strength, Dexterity, Constitution, Intelligence, Wisdom, and Charisma. These abilities can be generated in one of several ways. Using these abilities helps determine the general outcome of what I said above where "Players describe what they want to do." A player with a high strength will (generally) have an easier time knocking down a door than a player with low strength.
   
   Another stat is hit points. This is a pool of points describing the health of a player's character. When it hits 0, that player's character is in danger of dying.
   
   There are still other stats that define or influence how easy it is for a player to hit monsters and what kind of damage they inflict, as well as how easy it is for monsters to hit and damage players.
   
   The things that affect these stats are the player's race (fantasy tropes such as human, dwarf, elf, halfling), class (such as fighter, rogue, cleric, wizard), equipment and skills. Races grant some special abilities and stat adjustments. Classes define even more special abilities. A wizard is good as casting a wide variety of spells... whereas a fighter is typically better as dishing out combat damage. Player's will more than likely also find equipment that add other special abilities and / or make stat adjustments. If you've read or watched the Hobbit, think of Bilbo's sword "Sting". That granted him the ability to 'see' when dangerous goblins were nearby. Skills are specializations that the player can take that help influence the outcome of "what they want to do".
   
   As player's play, they gain something called Experience Points, or XP for short. As they accrue more and more experience points, they "level up". When a player's character gains a level, it typically means that they are granted some new special abilities. The player's level also influences a stat called the "Proficiency Bonus". This bonus also affects the general outcome of what players "want to do".
   
   Here's a super-brief example of gameplay bringing some of this together:
   
   DM: You see a large, aged pillar in the room before you. It stands in a pool of dark water. You can barely make out what appear to be scratches on the cracked surface.
   
   Player 1: What are the scratches? Do they appear to be writings or claw marks?
   
   DM: They appear to be writings, but they are too far away for you to read.
   
   Player 2: I ready my sword. Does the pillar go from the floor to the ceiling?
   
   DM: Ok. You have your sword in hand. No, the pillar stops short of the ceiling by a couple of feet.
   
   Player 1: I approach... cautiously. I don't want to run headlong into trouble.
   
   DM: Give me a perception check.
   
   Player 1 (rolls d20): 10! Adding my Wisdom modifier and Proficiency bonus gives me a grand total of 13.
   
   DM: Ok. As you walk toward the pillar, you notice ripples from the far side of the pool advancing towards you.
   
   Player 2: Oh, crap.
   
   ... etc ...
   
   Do you need to buy anything to try it out? Probably not. There are basic PDFs available on the Wizards of the Coast site that have a good portion of the rules. About the only thing you will need outside of those are some polyhedral dice, some pencils and paper, and two or more players -- one serving as the DM and the others serving as players. My personal opinion places the sweet spot of players at 5 or 6. That translates to one person as DM and 4 or 5 players as characters.
   
   The D&D Starter Set is a great gateway into the game. It presents the rules found in the basic PDFs, includes a ready-to-run adventure that has some hand-holding for the first-time DM, and includes a set of dice.
   
   Hope this helps!!!