Turn on your Wii and TV. Go to the main screen for Brawl.
Start by clicking on "Solo" and "Training."
Choose a character; Link, Kirby, Pikachu, Mario, are recommended. Play on the "Battlefield" stage (upper left) using a basic Wii remote, held sideways. The and buttons should be by your right hand, and the Control Pad (the , , , and buttons) should be by your left.
Start by moving around. Press the right and left buttons on the Control Pad to move right and left, press up on the Control Pad to jump, or tap down on the Control Pad while on a platform to pass through it. Most characters can only use two jumps while in the air, but characters such as Kirby, Meta Knight, and King Dedede can use five midair jumps. Charizard can jump 3 ×.
Next, try using basic attacks. Press the 2 button to use a standard attack. Also, try attacking your nonmoving opponent with standard attacks while moving to use a different attack. When using a GameCube controller, a Classic Controller, or a Wii remote with a Nunchuk, press the button instead.
Another type of attack is a special move, also covered at SSB Brawl Info. To use a special move, press the button. Each character has four special moves, and no two characters have the exact same set of special moves (even though the Star Fox characters are pretty similar, and Link and Toon Link, and others...). The four types are: standard special move, by pressing 1 without moving; side special move, by pressing while moving sideways; up special move, by pressing while pressing up (not necessarily jumping); and down special move, by pressing while pressing down. Most up special moves can be used for recovery (see below). When using a GameCube controller, a Classic Controller, or a Wii remote with a Nunchuk, press the B button instead. You can also grab another fighter, by using the and with Wii Remote with Nunchuk, with Wii Remote, with controllers.
To kill an opponent, knock them hard enough off the stage that they fly off the screen. You will notice a percentage meter at the bottom of the screen which increases with every hit taken; the higher a character's percentage meter, the farther they fly when hit.  You will also notice that if the CPU character is not killed, they will jump back up to the stage. This is called recovery, and is vital when trying to return to the main platform of a stage after being knocked off. When knocked off, use both or all air jumps and then, mostly, your up special move to get back to the stage. Try jumping off and returning to the stage.
Items are a key part of Smash Bros. Press +(or Start on the GameCube controller or the classic controller) to pull up the Training Pause Menu. Go to "Items" and click on "Beam Sword." Use a standard attack to pick up the Beam Sword that appears. That is how to grab an item. To use an item, also use a standard attack. To drop an item, use a grab(see later; for now, with the basic Wii remote, press 2 while holding B). Other basic items include the Fan and the Star Rod. Next, try using a power-up item. Get a Bunny Hood, and try moving and jumping. Other power-up items include the Franklin Badge and the Super Mushroom. Last, release a Smash Ball. The Smash Ball will fly around the screen, and you need to beat it until it breaks, at which point you will begin to glow. While glowing, use a Standard Special Move to perform a Final Smash, a powerful, unique, attack. For a detailed list of all items click here.
Next, get familiar with the game. Play 5 Brawls to unlock Ness, beat Classic to unlock Marth, beat the first 10 or so Events, play a bit of Stadium, use the Coin Launcher to get some trophies, and check out the Challenges screen to see what you need to unlock.
Now, you can go one of two paths. You can become a better fighter in the basic mode, or you can clear Adventure Mode: The Subspace Emissary. Either one is fine, and you will have to do both eventually, but the order you take care of them in matters. The first will be covered here, but that does not suggest that it comes before the other.
Go back to Training Mode. By this point, you should have gone to Controls in Options and seen the controls for Wii Remote with Nunchuk, GameCube controller, and Classic Controller. If you want to advance, you should have already switched to one of these three. The GameCube controller is recommended, but a Wii Remote with Nunchuk or a Classic Controller work just as well.