The game is very much about trial and error. Don't be afraid of trying stuff out. If you don't want to waste time restarting a new fortress, don't be afraid to save scrub (make multiple copies of your save game files). I'm massively guilty of that one.
Just on the level of getting a fortress which is reasonably self sufficient though.
1. Embark.
Never choose a site with an aquifier unless you want a massive challenge.
Calm and Serene regions will make for a nice relaxed game.
Joyous Wilds and Savage regions will make for a slightly more exciting game. Wildlife is not quite as deadly as it used to be, but you may still find the occasional dwarf gets nommed by a hippo.
Terrifying regions can live up to their name.
Some skills are more useful to embark with than others. Mining is essential (and make sure you bring some mining picks!) Having a dwarf with growing, brewing and/or cooking can help you get food production up and running quickly. Treecutting, woodwork and masonry are useful. Stonecrafting is very useful, I'll explain why later.
2. Food and drink production.
There are whole range of ways to get food, but the real issue is getting drink. Dwarves are alcoholics, they drink a lot more than they eat, and if they run out of alcohol they get surly and suffer a massive drop in efficiency. Don't try and survive on water unless you're going for a challenge game.
To make food and drink you need to grow crops.
Crops come in two varieties, underground and above ground. To farm, you need either soil or stone which has been splashed with water. The latter is complicated, the former is very simply as almost every map will have a soil layer. Dig out a room and put a field in it. If you accidentally dig into stone, your farmers won't be able to plant seeds there. A starting fortress does not need a very big farm, it's very easy to overproduce on food and fill your fortress with stinky rotten vegetables. Press Q, move the cursor over the field and select crops to grow in spring, summer, autumn and winter. Leaving the field fallow has no advantages, unlike in real life, but it does help you control overproduction.
Plump helmets (an underground mushroom crop) are the staple of the dwarven diet because they're so flexible. Hungry dwarves will eat them raw. If you build a still you can turn them into dwarven wine, and if you build a kitchen you can cook them into prepared meals which are more efficient at feeding dwarves than just eating raw mushrooms.
Incidentally, if you realize you forgot to take a certain skill and can't wait for the right immigrants to come along. Press V, move the cursor over a dwarf. Press P to bring up the preferences menu and L to bring up the labour menu. You can now choose exactly what tasks that dwarf will do, regardless of whether he or she is skilled in them or not. This way, you can eventually train useless peasants into productive members of society.
Once you've built a field and chosen what you want to farm, dwarves with the 'growing' skill should automatically start planting the right crops assuming you packed seeds. All you need to do now is designate a food stockpile by pressing P and then F and dragging out an area, and your dwarves should automatically store the crops there in any loose containers. Again, by pressing Q you can customize stockpiles, which you don't need to do now but is very useful later on.
3. Trading.
Early on, your fortress will not be very self sufficient. For this reason, trading is very useful. Various caravans will arrive, with the most useful being the dwarven caravan from your home civilization.
This is why I always bring a max level stonecrafter. As your miners mine, you'll notice they leave tons and tons of stone lying around cluttering the place up. If you build a craftsdwarf's workshop, tell it to make rock crafts and press R to make the action repeat, your stonecrafter happily carve away making all kinds of tacky crap like rock crowns and figurines which you can sell for far more than the basic stone its made of.
Another good thing to make are large pots. Again, these are made out of rock, which you'll never run out of. Food production requires a lot of containers, which means either pots or barrels. Building a decent supply will help keep your stockpiles looking tidy, will avoid rotting food and will ensure you can always produce booze.
To trade with the caravans, you need a trade depot and a broker. For the broker, press N to bring up the noble screen and pick whichever dwarf has the best social skills (or any random dwarf if none do) to be the broker. To use the trade depot, press Q and move the cursor over it. The rest should be self-explanatory.
Umm.. yeah.. there's a lot more to cover, but if you set up farming, buy all the useful stuff you can and if nothing goes horribly wrong you should make it through your first winter. Beyond starvation, the biggest cause of early fortress death is unhappiness, which is based on a huge number of variables. Most are common sense though, if you build your dwarves nice bedrooms and put pretty statues and furniture around you'll find they're much more emotionally stable than if you just let them sleep in the mud, for example.
Just remember, even once you've mastered the basics of keeping everyone alive and happy, it's highly likely your first goblin siege will steamroll you. Dwarf fortress does not have a learning curve, it has a learning cliff with tiny little ledges which crumble as soon as you try to stop for a rest.
But eventually, you'll watch a bunch of goblins and trolls being eviscerated by bridges full of traps suspended over a lava pit and you will think back on all the fortresses you lost and smile.
