Important basic controls:
Double clicking a monster will automatically attack them. Alternatively, selecting a monster and pressing 3 will also attack them.
Holding Control (Ctrl) and double clicking a player will enable PK mode and attack the corresponding player. However, killing someone over 4 levels under you if you initiated the first attack will net a Rogue Point. Rogue Points are bad.
You can use the mouse to move, or you can use the WASD keys to move. The arrow keys (quickly) turn the camera.
Holding the right mouse button will allow you to move the camera manually.
Double clicking with the right mouse button will allow you to move to the target spot. This is especially helpful if you use the mouse to move and you're traveling through a highly monster-infested area. This way, you don't accidentally attack a monster.
On the left side of your HP and MP bar are two arrows. If you slide these over to the right, a HP or MP potion will automatically be used once your HP or MP drops below the arrow. Thanks to Special for pointing this out to me.
Dragging a Magic Stone or a Prayer Stone to an unequipped piece of equipment will attempt to socket the respective Stone into the item. You will lose the Stone if it fails, but not the item.

Basic Chat Protocols:
No /command - Normal chat.
/s - Shout. People within a certain radius will hear you.
/w - Whisper. Send a private message to someone with /w charactername.
/p - Party. Send a message to your party members.
/g - Guild. Send a message to your guild members.

The Auction House:
The best way to get better equipment, and to sell some equipment you don't need, is the Auction House. Here, often times, commonly found items are sold cheaper than a regular weapons or armor merchant would sell them for. It is also a great way to acquire rare/unique armor and weapons.

It is usually best to check the Auction House to see the average price a piece of equipment or an item sells for. Obviously, if you want to try and sell something quickly, you'll sell it for less than the lowest price. Remember, not everything can be listed in the Auction House.

To list an item in the Auction House, open your Inventory, click the Sell button in the lower right corner, and drag anything you wish to sell in the window that pops up. If you drag a bulk set into the window, the price you set will be for the entire bulk, not for each individual item in that bulk.