The Basics
DotA 2 is an action strategy (or ARTS) game. It is often called a MOBA (Multiplayer Online Battle Arena), a term coined for the game League of Legends, but use of the term is somewhat controversial within the Dota community.
Two teams of five players face off against one another on the map. The primary objective of each match is to destroy the opposing team's 'ancient', which is located at the heart of their base. The ancient is defended by three tiers of towers, as well as basic AI-controlled units called creeps which spawn at regular intervals, and the five characters controlled by the opposing team.
Heroes
The player-controlled characters are called heroes. Before the game commences players choose their hero from a pool of over 100 heroes (the method of selection varying depending on the game mode). Each character has a health pool and a mana pool (which is used to cast their skills).
These heroes are divided into two main factions: Radiant (the 'good' side) and Dire (the 'bad' side). Within these factions the hero pool can again be divided into three different groups which are based on the heroes' primary attribute: Strength, Agility or Intelligence. Strength heroes tend to be more durable, Intelligence heroes more spell-reliant and Agility heroes more flexible.
There are also a number of different groupings based on the roles each character plays out in-game. Some characters, for example, can be classed as 'support' heroes (i.e. heroes which, when played correctly, will use their spells and gold to aid the more important heroes on the team), others as 'carries' (heroes which deal huge amounts of DPS (damage per second) later in the game), and so on. There are a number of different 'roles' in the game (some of which are disputed, such as the concept of a 'tank').
The goal, in more competitive games, is to draft a balanced team which will counter the opposing team during the game itself.
Gold
Once in-game, the goal is to destroy the opposing team's ancient. In order to do this you must first make your hero stronger.
At the start of the game you're given starting gold, with which to buy some basic items from the shop at your base. You will then need to level up your hero and acquire more gold for more expensive items. This is done by killing creeps (either in what is called 'the lane' where there are enemy creeps or in 'the jungle' where there are neutral creeps).
In this laning phase you will typically compete for last hits or denies (which results in the opposing team getting less experience and gold) on the creeps with members of the opposing team. By last hitting a creep you acquire more gold, and each creep that dies within experience range of your hero grants you experience which levels up your hero.
You are also granted gold is you manage to kill one of the opposing team's heroes (and likewise lose gold yourself if they manage to do). Doing so also slows their progress and allows you to gain the upper hand as your transition to them middle stages of the fight.
Gold allows you to buy stronger items and, as the game progresses, the two teams will tend to group up and fight against eachother in large-scale skirmishes once they've acquired some of these stronger items. A number of factors go into determining which team will win a fight, including the hero composition, levels, items, and player skill.
Skills
The acquisition of gold is just one half of the short term goal in the early stages of the game. The other is the acquisition of experience, which allows you to level up your character. Each character has a level cap of 25 (which more often than not is not reached in a typical game).
Every time you level up your base stats are increased and you are given a single skill point which you can invest in one of your skills or in more basic stats. Each character has its own unique selection of skills to choose from (most characters have 3 main skills and 1 'ultimate' skill, which tends to be much more powerful than the others and can only be levelled up when you hit level 6). These skills can be assigned to hotkeys on the keyboard (the default ones being QWE for the regular skills and R for the ultimate).
Any example of one character's skill menu (and their items) is shown below:

The skills can vary wildly from one player to the next, but most will fall into either being offensive spells which can be used to damage the enemy, or defensive ones, which help protect your own character or your teammates.
Roshan
DotA also features a boss-like creature called Roshan. Extremely hard to kill in the early stages of the game, even during the mid-game Roshan will usually require several team members to bring down.
The reward for defeating Roshan is that each member of your team is given 200 bonus gold and Roshan drops an 'Aegis' which will allow the player carrying it to die once without a penalty and respawn where they died after a short delay.
Roshan respawns randomly once every 8-11 minutes and, if killed three times, will also drop Cheese, which instantly restores health and mana when used.
The reward for killing Roshan is therefore quite high, and so battles will often take place around his pit as teams vie for the ability to kill him and gain bonus gold and an Aegis.


