Hello, and welcome!
Well, as you can see from just looking at the book, a lot has changed, and a lot will seem counter-intuitive. Things to keep in mind...
(1) What would have been a small or insignificant bonus or penalty in 3.x makes a huge difference in 4e. A +1 to-hit is a big deal. A +1 to defenses is a big deal. This is all because DCs are usually set to give you somewhere approximating a 50% hit chance.
(2) By the same token, most bonuses and penalties have been reduced. As an example, Charging is a +1 bonus, and Cover is a -2 penalty.
(3) Almost everything follows the basic progression of (1/2 Level + Ability Modifier + Misc). This includes attack rolls; those are no longer the main source of difference between combatant and non-combatant classes.
(4) The difference in classes is found in their special abilities and in their powers, not in the math behind those abilities and powers. On paper, a Wizard and a Fighter may look fairly similar - both have similar bonuses with their main attacks, their ACs won't be too far apart, and the HP difference might be 50% instead of 100%+. In play, they work intensely differently, and you couldn't possibly mistake one for the other.
(5) Your At-Will powers are part of the way your class is defined. Ideally, you will almost never make a Basic Attack. Use an At-Will power whenever possible.
(6) As a general character-creation note, if all you're using are the core 3 books, don't spread your stats too far out. You want, after modifiers to have at least a 16 in every stat you'll be attacking with. An 18 is honestly ideal. So, if you're a Cleric, Paladin, or Warlock, try and focus on one of the two main attack stats. (Every class since PHB1 has had only one main attack stat, and two or more secondary stats for "rider effects.")
(7) If you're starting from Level 1, grab the character builder! It's pretty awesome.
...more as I think about it.
I hope you get a kick out of it!
-O