IF YOU ALREADY HAVE WARCRAFT AND IT'S EXPANSION INSTALLED ALONG WITH THE LATEST VERSION OF DOTA AND HAVE ALSO CREATED A BATTLE.NET ACCOUNT
Install Warcraft 3, The Frozen Throne, and the latest version of DotA.
Before logging on to Battle.net, make sure your options are set so that the game runs smooth (however, I suggest keeping "spell detail" at at least medium or else some of the smells will look much different than they normally do). I also suggest going into gameplay options and checking the box next to "Always showhealth bars", this is important, as it allows you to see how much health a unit, hero, or building has without clicking on it or holding the alt-key. Once you have your settings set, you will probably want to load up the DotA map in single-player mode in order to familiarize yourself with the item locations, what they do, the lay of the land, and the various spawn times. Visit www.dota-allstars.com and http://www.dota-allstars.com/wiki/DAWiki:Main_Page for quick info.
Once you have your settings set, you are ready to log on to Battle.net and make your account. Be sure to play on the gateway that is closest to where you live, this will allow you to join games created by people who live close to you, and thus reduce lag. After you have created your account you are ready to start finding games on Battle.net. Starting out you will want to play public games, that is, games which have been created for anybody to join. These games will usually have names like "DOTA -APEM 5v5" or "Dota 6.59d -arem Pros ONLY". The letters you see after the dash indicate the game mode that the host plans on using. AP means "all pick" and indicates that you can pick from any of the heroes the game has to offer; EM means "easy mode", and is a mode where you get extra gold and buildings are weaker (I suggest avoiding this mode as the extra gold you receive will make you less reliant on your own ability to farm.); AR means "all random", and is a mode where everyone is given a random hero; RD stands for "random draft", and is a mode where everyone takes turns picking from a random pool of heroes. There are many other modes, but these are the ones you are likely to encounter in public games. When you find a game you would like to play try to join it, if its not full you will find yourself in a lobby with other players. Hosts will often kick players who don't have the map already downloaded, so make sure you have it downloaded before you start joining games. Hosts will also often kick players with high-ping, so if you are currently downloading something, you might want to turn it off so that your ping doesn't appear high (if you have 56k, you might find yourself getting kicked from a lot of game lobbies). Once the game is full the host will start.
Once the game finishes loading, you will find yourself without a hero. After the hosts enters the game mode though, you will have the opportunity to either select your hero if the game mode is "AP", be given a hero if the game mode is "AR", or select a hero from the random pool when it is your turn if the game mode is "RD". Whatever the case, the hero that you get is not important when you first start playing DotA. While you might get "yelled" at for picking a "bad" or "cheap" hero, or for ignoring the hero needs of the team, starting out you should be focused on learning the flow and intricacies of the game.
After you have your hero, it is important to get starting items. The number one rule of getting initial items, is to ALWAYS GET REGEN. I repeat, ALWAYS GET REGEN. By regen, I mean a way to heal your hero. You can get regen from several different sources, tangos of essifation, healing salves, a bottle, rings of regeneration, or from the abilities of your hero. After picking your hero, it is important that you decide how much regen you will need. Some heroes like Earthshaker are better off with a decent amount of regen at the start (at least a couple of healing salves) because he is melee and has no natural health regeneration ability, this means he is a prime target for getting harassed in the lane. Other heroes like Enchantress don't need much early game regen because she has a natural health regeneration ability (though on a hero like her, you would probably want to get clarity potions so that you could regenerate your mana) and is a range hero. When getting regen you should also take in account how quickly you will be able to farm additional regen like a bottle or ring of regeneration/health. On a hero like Kunkka, who is great at getting last hits, I often don't get a lot of regen starting out, because I am confident I can farm a bottle or ring of health quickly. This all might be confusing at first, but eventually you will feel comfortable knowing how much initial regen to get on the various heroes of DotA. After you have an adequate amount of regen, you should begin getting stat-boosting items such as circlets, Ironwood branchs, slippers of agility, gauntlets of strength, and mantles of intelligence. The combination of aforementioned items that you should get depends on the main attribute of your hero, along with his/her HP and mana needs. Make sure to spend as close as possible to all your gold.
After you have your stat-boosting items (which should all either contribute to the main stat attribute of your hero, or alleviate a weakness such as low hp or mana, don't worry about armor) then you are ready to head to a lane. Make sure you always get to one before the creeps spawn. Starting out you probably want to be paired up with somebody, as being the only hero in a lane (known as soloing) is a big responsibility. This means you will either head to the top lane or bottom lane, as mid is generally reserved for the solo hero. Look at who your lane partner is to get an idea of how things will play out. If you are with a hero that can stun, and you also have a hero that can stun, you can play more aggressive. If you are with a hero that can heal, and you have an agility hero that is fragile but does lots of damage, you can try to farm up while they keep you healed and safe. As you continue to play DotA you will learn the hero combinations that work great, and the hero combinations that are destined to fail.
Once your creeps engage the enemy's creeps, the game has truly begun. Make sure you are aware of the heroes you are laning against, and what they are capable of doing. You should always know how aggressive you can get or how passive you will have to be against the opposing heroes. It is at this stage of the game that you should focus on last-hitting (killing creeps so that you get gold), denying (killing your own creeps when their health drops below half so that your opponent can't get the gold/experience), and harassing (attacking the opposing heroes so that they will either have to go back to the base and heal, or lane with low-hp. Last-hitting should generally be your first priority, harassing your second, and denying your third. Priorities can vary, however, depending on your hero, and the heroes that you are laned against. Remember to only hit opposing creeps when your attack is going to be the fatal blow. Doing this will keep your creeps from pushing out from the safety of the tower too much. Avoiding attack moving (letting your hero continuously attack and select targets) and only last-hitting is one of the first and most important things you should master in order to get out of the "noob" phase. If your creeps get pushed past the river, then you are more vulnerable to ganks (heroes coming and outnumbering you, or killing you while you are low). It is also important to start hitting your own creeps when they are under half hp, without letting the enemy finish them off or letting last-hit opportunities past you by. Remember, denying is your last priority. Killing the opposing team's creeps while taking minimal damage is your first. Try to stay in your lane and farm for as long as possible. You do this by not letting your opponents get continued hits on your hero, and by using your sources of regen when you get weak. Be aware of the location of other heroes around the map, if you see an opposing hero missing from mid, and you're bottom, then you probably want to play passive and stay close to your tower until you see the missing hero appear back on the map. Always keep one eye on the mini-map, it is your best friend and constantly checking it will help you avoid being an easy target.
Eventually you and your lane partner might want to kill the opposing heroes in your lane, this usually happens at agreed upon level where you both feel like you can kill them without dying in the process. Before attempting to kill the opposing heroes, think before-hand how you will do it, and whether you will be able to enough damage to overcome their HP or defensive spells like Omni's "Purification". Many a player has died in the process of going for the kill by forgetting about the opposing team's abilities. If you don't feel like you and your lane partner can kill the opposing heroes, then you can either ask one of your teammate's to come help, or continue farming if you are vastly out last-hitting and denying your opponents. Remember to get items by either walking back to your base, or preferably by using a chicken to bring them to you. Go to the www.dota-allstars.com forums for help on what items you should be getting.
Eventually the flow of the game changes and you might have to start ganking or pushing if your hero is suited for such activities. When ganking other lanes, always be aware of your visibility. You don't want to stand around in a spot where the other team can see you, and begin running before you begin your attack. Also make sure to check how much health and mana your allies have in the lane you are about to gank. Don't go running in to gank, only to find out that you allies have no health or mana, and thus no way of contributing.
Eventually by winning a large-scale battle, or by picking off enemy heroes who are alone or in smaller groups, you and your team will be in a position to push without resistance. Push with your team until the enemies heroes revive, however, if you can kill them again, by all means do it. Just don't let them kill you all, and allow them to counter-push. Keep killing heroes as a team then pushing, or pushing then killing heroes when they come to defend. This is of course easier said than done, and vastly simplified, but if you and your team have the level and item advantage, this is how you will eventually win.