When you are assigned a quest, your first step is usually going to be to find the location you must go to. Most commonly this will be a dungeon and with very few exceptions, it will always be in the province where you accepted the quest. In order to find the location, you have to understand the overland map.
You bring up the overland map by either right-clicking on the map icon on your toolbar or by using the "W" hotkey. The map that comes up is a map of the Iliac Bay area with the provinces outlined in yellow/gold. The first time that you do this in any gaming session (a gaming session starts when you launch the game and ends when you exit to your operating system), the province you are currently in will flash red two or three times. After that you can locate your province by clicking the "I'm At..." button. Left clicking on a province will bring up the overland map for that province. A set of red crosshairs will mark your location on that map (assuming you are in that province). If you forget where you are, click "I'm At.." and the crosshairs will flash again. On the overland map are lots of little dots. The color of the dot tells you what it is.
Most of the dots will be varying shades of gray with a few white ones thrown in for good measure (on some systems and in the zoomed view they show up as pink/purple). These are cities, towns, villages, inns, and a few individual farmsteads. The closer to white the dot is, the larger the settlement. White dots are always walled towns (gates open at 6am [6:00] and close at 6pm [18:00]). Dark gray dots are farmsteads. If you move your cursor (the light blue arrow) next to one of these dots, the name of that location will appear at the top of the screen. Clicking the "Towns" button on your map toolbar will toggle these on and off. By the same token, clicking "Homes" on your map toolbar will toggle the inns and farmsteads on and off.
Blue dots are temples. All of them belong to the same god or goddess (depending on the province) and most of them are nothing more than a temple building with a half-dozen or so houses around it. Clicking the "Temples" button on your map toolbar will toggle these on and off (I usually toggle them off unless I pick up a disease while dungeon crawling and there is no town nearby).
Orange dots are dungeons. When you first start the game, the only orange dot will be Privateer's Hold (the dungeon you start in). Reddish-orange dots are dungeons that you have not visited (this part doesn't work consistently, but it's a good rule of thumb). Clicking the "Dungeons" button on your map toolbar will toggle these on and off.
Red dots are graveyards. For more about them, read the section on "Crypt"-ology. Clicking the "Dungeons" button on your map toolbar will toggle these on and off.
Black dots (there are none at the beginning of the game -- you must either find a map or cheat to get these locations) are Witch Covens. You might want to visit one of these if you need to summon a Daedra or get cured of Vampirism or Lycanthropy.
To find the location of your quest, use the "Find" button on the map toolbar. A box will appear asking for the name of the location. Type it in (watch your spelling - many locations have similar names) and hit "enter". The crosshairs will mark that location and the fast-travel menu will pop up. If you get a message saying "There is no such place on your map", you have probably misspelled the name (did you know that "misspelled" is the most commonly misspelled word in the English language?) or you have run into an old bug that hasn't been properly fixed (sometimes quest locations do not appear on the overland map). If you are sure of your spelling ("Ruins of the Ashham Farmstead" is not the same as "The Ruins of Ashham Farmstead"), you need to exit the map and hit <ctrl>+f1. If you are running the v.212 or v.213 patch and have "cheatmode" enabled, this will make ALL dungeons and covens appear on your overland map. Bring up the map and try again. The crosshairs should mark the location for you now. Once you have travelled to your destination, hitting <ctrl>+f1 again will toggle the unvisited locations off again, but yours will remain because you have visited it. This cheat will also put you into "steal" mode, which means you're going to try to pickpocket the next person you talk to unless you chage it. Be cautious.
After you find your destination, you need to choose your travel mode. "Cautious" will have you arrive at your destination with full health, fatigue, and spell points and while the gates are open. "Reckless" will not restore points, but will get you there in the shortest time (which might mean arriving in the middle of the night). "Foot/Horse" is the default but trips across the bay can be speeded up by choosing "Ship" ($$). If you own a horse and a ship, you will always take the quickest route. "Inns" means you stop at an inn every night and eat there (at 5 gp per night), while "Camp Out" means you will sleep under the stars and hunt for your food (costs nothing, but slows you down a little).
Tom Stabler pointed out something that I had not included (all I can plead for not including it is encroaching senility). If you choose "Reckless" mode to get to your desination quickly and then use "Cautious" to travel to your current location, you can have the best of both worlds: quick travel time and full points when you get there. The same applies when traveling to towns: "Reckless" will get you there quickly, but follow it up with "Cautious" to restore your points and make sure the gates are open.