Hello!
Some people have pointed this out, but I think it should be stressed again, as it seems to be an important piece of advice:
Dwarf Fortress is a game you can not win as there is no winning condition or anything. There is not even a score system, although you could argue that adventurer mode actually has a score system in the form of legends mode.
Thus, reaching a game over situation is not necessarily a bad thing, as you can not fail at reaching something that is not there anyway. Yes, you lose the chance to continue playing that particular fortress or that particular adventurer, but beyond that, you have not lost the game.
With this in mind, I think it is important to see DF, especially in dwarf mode, as a game of exploring. For the first one or two years of playing it (just kidding :) :) :) ), you will be exploring just all the possibilities in the game. What you can do, how you can do it, and how you can do it differently. And then, you will be doing more and more exploring of the worlds you have created, accessing their histories, their culture, enjoying all the diversity that has gone before your playing.
So, in a way, DF is the embodiment of the way being the goal.
Thus, never worry about failing; just go with the flow and have fun. And if you have any problems or are confused, don't be shy, ask the community for help.
Yours,
Deathworks