If you are just curious about the game, there are many "Let's Play Dwarf Fortress" videos on YouTube. Expert players talk through the game features and progression.
Tim Denee's two infographic/comics on his [1]Bronzemurder and [2]Oilfurnace fortresses were what finally convinced me to take the plunge.
I knew basically nothing of the game, so found a random [3]step-by-step tutorial and actually did pretty well until I accidentally killed the mayor, several other nobles and half my standing army at the grand opening of the new great drawbridge due to a...Minor malfunction.
The biggest three tips I can give are:
A. get a texture pack. I'm sure many people love the ASCII, but actually seeing dwarf and goblin icons removed one more thing for me to learn at the beginning.
B. download Dwarf Therapist. It's a great external UI for managing the roles of your dwarves.
C. don't be afraid to fail, because you will. Often.
That bronzemurder story is fantastic, I started playing DF the other week and although I move and plan quite slowly, it's very fun.
I'm actually building on a pregenerated world right now where there are 2 cliff faces and waterfalls across from each other. Aquifer's are really annoying though.
Do you know of any texture packs that don't make the map 'zoom' level extremely high? Most of the texture packs seem to be made for large and specific resolutions, I play a smaller window mode on mba (1366x768).
Thanks to that tutorial I made absolutely sure my starting point was aquifer-free, but I might try with one at some point just for the challenge.
I use Phoebus' Graphics Pack on my 1024x600 netbook and it seems ok, but I'm pretty used to a tiny screen and resolution so it might not be what you're after.
To get a great flavour of dwarf fortress in a longer written form. You can't go wrong with boatmurdered, which is a game where each player took a year (I think) of playing the fortress and then handed on to the next player to pick up the pieces and carry on.
http://lparchive.org/Dwarf-Fortress-Boatmurdered/
Unfortunately, I don't think that Dwarf Fortress is a game that is enjoyable if you just look at someone else playing it. There's too much little stuff going on in the screen to figure out what the big stuff is and the pace of the game can be slow. There are a few good video tutorials, though.
Just try the game.
edit: there are some tools you can use to visualize your dungeons and what is going on there. There might be nice videos of some 3d-renderings of fortresses that might be nice to give you an idea of the game.