If you're reading this for information, I will assume you haven't actually started playing yet, so refer to the screenshot on the right for a basic layout of the user interface. The screenshot use the basic UI, with no mods or add on to modify it, so this is what your screen will looks like when you first log on.
The first thing you will witness is a brief introduction to your race, purely for storytelling purposes. The quests you do will often relate back to what is mentioned in it.
When you first look at the screen and all the stuff on it, you might be a little bewildered. Let's talk about what's on the screen right now, and get into the menus a bit later.
In the upper-left corner is your character portrait, along with your health and mana bar. (or rage or energy, but I will continue to say mana.) If you were in a group, your groupmates' display would appear below your's, slightly smaller.
Next to your health is your target's health. You will need to click on someone or something to get a target, but in the screenshot, the priest is fighting a Highland Raptor. The red namebar indicates that this is an aggressive target. Yellow indicates non-aggressive, able to be attacked, but not aggressive. And green is a friendly target that you cannot attack. Player names are in blue. "Tapped" targets, which we'll discuss later, are in gray.
Just to the left of the minimap are active buff. This player doesn't have a
Above the bottom bar are the two chat windows. The right one is for combat messages and the left one is for all other messages, such as communication with players. This is no longer the default setting, and you will probably not see the combat window by default, although it is easy to switch to by putting your mouse over the chat box and picking the other tab. (The current set up is refered to as "simple chat" in the interface options.)
Along the bottom, the left side of the bar indicates abilities that can be used at the push of a button, or you can click on them. You get six bars to work with, and there is no limit to memorized spells or anything like that. The only limitation is what you can fit on the screen, and some custom user interfaces create more bars of hotkeys.
The center region of the bar is the different menus you can bring up. The right side is your bags - you will start with just the backpack at the right end, and a quiver if you are a hunter. You need to acquire bags to begin with, and this is one of your first challenges in the game. The green bar between the options and bags is a lag-report, that gives you your ping if you mouse over it.
The long narrow bar divided up into 20 blocks above the toolbar is your experience meter. You can read all about experience elsewhere, but at low levels, it will fill very quickly. If you are considered "rested", meaning your player is fresh from inactivity, you may find a notch in the experience bar. Until you reach that point, you gain experience at a higher rate.
If you move near that person and right-click them, they will begin to give you a quest. That quest will either be to kill some of the basic creatures nearby, or talk to someone nearby who will tell you to do that. Be sure to keep an eye out for other questgivers. While you have an active quest with an NPC, they will have a silver question mark over their head, and it will turn yellow when you have finished. (A silver exclamation point means that person has a quest you are too low in level for.) Quest givers also show up on your mini-map.
You might have noted when you put your mouse over the questgiver to talk to them that your cursor changed to a talk bubble. Any time your cursor changes, there is something special you can do by right-clicking. Talking to people, looting corpses, mining ore, opening chests, and attacking monsters are all different examples.
Find a nearby creature, and walk up to them. You'll notice that the game tells you what level they are. Expect a tough fight if it isn't level 1 or 2. Target it and attack by either right-clicking the creature, clicking on the attack hotkey at the left end of your ability bar, or by pressing one to activate that hotkey. (You can also press T to do this.) Your character will attack automatically until the fight ends. Your skill with your weapon will probably go up some, and when the creature dies, you can then loot its corpse.
Find another creature, but this time, try using one of your abilities to start combat. If you are a melee character, such as a rogue, it will turn on auto-attack by itself. If you cast a spell or fire an arrow with autoshoot, you will need to turn on attack on your own when the creature gets near. You can also use your skills during combat, of course - a warrior will have to since he starts a fight with no rage and has to attack normally at the beginning (for now.)
After you've picked up some stuff, click on your backpack to open it, or press B. You might have picked up something you want to equip. You'll also have a few things you started with - some food and drink, your hearthstone, and a note from your class trainer. Food and drink restore your health and mana out-of-combat, and the hearthstone will teleport you to the last place you bound it to, (usually an inn,) with a one hour re-use timer. Right-click on the note (it might not be a piece of paper) and it will start a quest simply to find your trainer.
Go to your backpack and pick up an item you want to try equipping. One of the boxes in the menu should turn blue. Click on that box and your character will equip that item. (If the armor type is in red, such as mail for a priest, nothing will happen because you can't wear it.) If you replaced an old item, like your shoes, it will go where the new shoes were in your backpack. You can also right-click to quickly equip items. If you were lucky enough to get a bag of some sort, *drag* it to one of the other inventory slots in the bottom right.
There are two other tabs at the bottom of the character menu, reputation and skills. Ignore reputation. Skills will tell you the things you are capable of (weapon proficiencies, for example,) and how skilled you are at them out of your potential. Your potential will increase each level.
Press escape to close the windows you have open, and press M for map. This will bring up a map of the nearby area you are in. Not much of it is showing since not much of it is explored, but at least this should help you a little bit from getting lost. If you right-click on the map, it will zoom out to show the whole continent, and you can look at any other map you have explored.
Kill a few more creatures, and then go back into town (or whatever settlement you have) and find a merchant - any merchant. If you put your mouse over an NPC, it will say their name and their profession. Generally anyone that isn't a guard or a class trainer in the starting area will sell things. (If a person has a big name floating over their head before you target them, that is another player.)
Right-clicking on a vendor will open up a sell window. There might be things you want to buy, but hold off for now. Find a couple items in your backpack that you can't use at all, such as random body parts of creatures you killed, and left-click them to highlight and then left click in the list of goods to sell it. You can also right-click to sell quickly.
When you've sold everything you can't use, close the window and look around for your class trainer. They should appear as a yellow dot on your minimap when you draw near, but some might be a little tricky to find. (Night Elf druids and hunters: there is a ramp around the left side of the tree by the guard that leads up to where your trainers are.) Assuming you haven't already, you will finish your first quest by talking to your trainer. Right-click on them and pick complete quest. Voila, a couple free exp. (Next to none, but other quests will give far more.) When completing other quests, you will often get a choice of rewards at this screen.
In any event, talk to your trainer again, and tell them that you wish to train. There will be a very short list of abilities showing that you can train from them. (Your skills up to level 6, to be specific.) One of them will be green, meaning you can learn it now. Click on it and click train. Congratulations, you just got a new ability.
Now you will want to open your spellbook to make a hotkey for it so you can use it. Click on the book at the bottom of the screen or press P. The spellbook has 4 tabs - one for basic general stuff like attack and tradeskills you might have, and three for different class skills. One tab should be glowing. Click on it, find your new skill, and drag it to the toolbar.
Look around town for any other questgivers there might be. You should find at least two besides the very first one and your trainer. If you aren't sure how many quests you have or if you've completed one, you can look at your quest log by pressing L, or clicking on the chalice button in the menu bar. This will give you a list of all your quests, and give you the text of the one you have highlighted with your progress at the top. It also tells you who to report to when you finish.
Any quest you have finished will have its line ending in "(completed)". When you get higher level quests, they will appear in orange or red, rather than yellow, to indicate their difficulty, or if you let a quest grow old (by outgrowing it in levels,) it will turn green and eventually gray.
That should just about do it for your first five minutes, or more likely a tad bit longer than that.