Quick note on definitions:
Aspects are... aspects. They can be used for a +2 or reroll when they apply, and a Fate Point is spent. If a given aspect hasn't been used before, it can be 'tagged' for free ONCE (no FP cost).
Declarations are one of 3 or 4 ways to CREATE aspects... and the most direct way. A Declaration involves a player paying the GM a Fate Point to (more or less) become GM for a moment- long enough anyway to declare an aspect exists, and you're done. If the GM takes the FP, then that's all there is to it, bargain struck and kept.
Assessments allow a character to use a skill roll to 'discover' aspects that exist already, but that he's unaware of. They can also be used to create an aspect, like a declaration (without the FP cost), but only if the aspect is appropriate or close to one that should probably be there- this is the GM's call.
Maneuvers create an aspect because the character (not player) does something specific to cause it in-game, like turning a bright room dark, by shooting out the lights, or flipping the switch, and almost always requires a skill check (to successfully hit the light bulb, or reach the light switch safely in a gun fight)- only time they aren't required if they're trivial (because anywhere but a gun-fight, making someone roll to flick the light switch is silly, and takes away from the game).
Consequences are aspects that exist because you've taken too much stress to cope, but not enough to lose the conflict... mild are easily recoverable, moderate require some medical/social/psychiatric care (severe burns, emotional trauma), severe require a great deal of time and care (broken bone, PTSD, etc), extreme may never go away (like losing a limb).
But they still all create aspects, and then you use those aspects. (Remember- a freshly created or discovered aspect gets one free use.)
You can use an aspect in 3 ways, really- if it applies: Reroll, +2 bonus, or compel (this is more for the GM than the players, though I've seen them compel eachother).
A Compel is when someone points to a player and says "Hey. You're not playing your character right. If he's such a Loose Canon like it says on your sheet, wouldn't you be shooting your mouth off right now?" "Um... but if I do that, I'm gonna get my ass kicked." Then comes the carrot and stick- if he plays it like a Loose Canon- he gets a fate point... if he refuses, he pays one. It's a lot like oWoD (nWoD for that matter) and gaining willpower if your character stays true to his concept/nature/demeanor/etc... and being able to pay one to break away from it a while (since these respectively reaffirms/undermines their sense of self).
Players can also self-compel, if they're playing well w/o coaxing and the GM didn't notice.
[EDIT: This is all Fate stuff. Anything involving Fate Points or Aspects is part of the Fate system, and just allows things like scenery and personality to affect die rolls.
Fudge is the base system of skills, abilities, and dice rolls... which should be pretty easy to grasp given some practice, given how much experience you have with so many different game systems. It's closest to D20 in the skill+roll vs DC, but with lower skill/die/DC values, and a die roll that produces a bell-curve instead of a flatline. The only other significant differences are Streamlining of rolls (so attack and damage are handled in one roll, reduced by defense and DR), and addition of social and mental combat that follow the exact same rules as physical combat.]
Hope that clears some stuff up...
You can still do some pretty awesome butt-kicking in DFRPG, but the game tries to set things up so players don't have to limit themselves to dungeon grinds- I've never seen a system (even oWoD) handle social conflict as simply or importantly as DF.
If you want to watch a game- there are lots all over the place- and even some play-by-post games on here- it's not quite the same, but may help you out.