Ryujin
Legend
For your first adventure I would recommend that you try one of the pre-made ones available through Dungeon Magazine, that strikes your fancy. That should help you get into the rhythm of things and help you to write your own adventure. Starting cold might be a bit much, for your first outing as DM.
Every character can make skill rolls, but not every roll is valuable. Players will likely start tossing numbers at you for skills rolls you haven't asked for. Keep in mind that they only count for something if you want them to. To second surfarcher's comment, I find that my patented, "There doesn't SEEM to be anything going on." suitably annoys players
I also agree that a DDI subscription is a very useful tool. It keeps you up to date on any errata to the original books. You also get 5 monthly updates for Character Builder, which by some odd coincidence equals the number of characters in the generic party, and access to some useful online DM tools.
For the number of encounters in the average dungeon all that I can say is, "It depends." You can have an adventure that's over in an evening, like the Chaos Scar series, or you can have an epic series of connected battles that runs for a year. Just keep in mind that the players will typically need a 'programmed' long rest after an average of 3 to 4 encounters, simply because they'll have expended their resources. You should provide an area that they can safely rest in for this, that they can determine through the use of a skill like Dungeoneering, Nature, etc.. Or just tell them that it's safe
Some players get more out of it if they think that they are putting one over on you with respect to treasure so if your group is that type, include any value of monster equipment in your totals. Otherwise just tell them it's rusty crap, that's barely usable.
Lots of great campaign ideas in DMG2 including godly boons, companion characters, and much more.
Every character can make skill rolls, but not every roll is valuable. Players will likely start tossing numbers at you for skills rolls you haven't asked for. Keep in mind that they only count for something if you want them to. To second surfarcher's comment, I find that my patented, "There doesn't SEEM to be anything going on." suitably annoys players

I also agree that a DDI subscription is a very useful tool. It keeps you up to date on any errata to the original books. You also get 5 monthly updates for Character Builder, which by some odd coincidence equals the number of characters in the generic party, and access to some useful online DM tools.
For the number of encounters in the average dungeon all that I can say is, "It depends." You can have an adventure that's over in an evening, like the Chaos Scar series, or you can have an epic series of connected battles that runs for a year. Just keep in mind that the players will typically need a 'programmed' long rest after an average of 3 to 4 encounters, simply because they'll have expended their resources. You should provide an area that they can safely rest in for this, that they can determine through the use of a skill like Dungeoneering, Nature, etc.. Or just tell them that it's safe

Some players get more out of it if they think that they are putting one over on you with respect to treasure so if your group is that type, include any value of monster equipment in your totals. Otherwise just tell them it's rusty crap, that's barely usable.
Lots of great campaign ideas in DMG2 including godly boons, companion characters, and much more.