The let's play tuts are long, because the do just a normal game, only explaining a lot of stuff.
Lot's of it you won't need to start your own fortress.
Each tutorial has to start with the basics, that would be: Creating a new world, choose an embark location, and some of them also explain how to "prepare carefully", which means how to change skills of your starting dwarfs and how to buy different things to bring with you on embark.
Each tutorial also will explain some basic stuff regarding menus and shortcuts and things like looking around and explore the map.
Also, you will always see how to start a new fortress with digging basic rooms, building farms and basic workshops and stockpiles and so on.
All of this will usually be covered in about the first three videos of a tutorial series. I suggest, you just watch a bit and read the starting guides at the wiki and then try it yourself. There is now way of learning the game completely by watching a few videos.
You will encounter problems and question will arise every so often. Then the wiki, the forums, and youtube are your friends to help you.
Part of the fun is actually to learn the game and to fail (on epic proportions!) and to try to get around the difficulties or avoid them in your next fortress.
Always a good starting point are captnduck's videos:
http://www.youtube.com/watch?v=iHVZtRdtPdo&list=PL06686270DA5FF439Also, though a bit outdated in some aspects, TinyPirate's tutorial is still very helpful:
http://www.bay12forums.com/smf/index.php?topic=31928.0