A couple bits of advice:
First and foremost, don't be afraid to fail. Remember, "Losing is fun". A lot of the best and most memorable stories involving this game are all about the mayhem as a fort crashed and burned. Since the game generates a semi-persistent world for your forts, a failure is just another interesting place to go explore in adventure mode.
With that in mind:
The wiki will be your best friend for a good long while. It goes into deep detail on a lot of the more complex points of the game, and is a pretty fair source of strategies for both beginners and advanced players. If you run into a mechanic that is confusing you, there will probably be a page somewhere on this wiki that explains it.
The two most likely failing points for your first fortress will likely be booze and food. Your dwarves prefer to have a large stockpile of alcohol available, and will be slower and less happy without it. Even worse, there are maps where your only good source of drink will be alcohol, so if you don't have enough you will lose dwarves to dehydration. So early on, figure out what you need to produce food and booze, and you will have a much smoother run.
If you make it the first couple years, your next major threat will come from goblins. They will come in either small hidden groups, or large visible sieges. Either can kill you if you aren't careful. While I consider a strong military to be the most fun way of dealing with them, it is also fairly complicated to get up and running. Instead, look up the page on traps, and build a whole bunch at the entrance of your fort. If you have enough, the goblins will take such heavy losses from them that they will retreat.
Once you're experienced enough to deal with these, you're probably be advanced enough to figure out the rest on your own.