The bright wizard cancels the effect of an action just used. I'm confused about this because of previous games i have played. Which part of a cards game text is the cost of triggering the action and which part is the effect?

For example if the wizard was to target another wizards effect, would the controlling player get the 2 resources back as the whole effect is cancelled?

My interpretation is that they wouldn't because if the resources were paid on resolution the a player could trigger the effect even if they have no resources remaining.

Is there anywhere in the rulebook that defines cost and effect of triggered actions. The actions section of the rulebook says that costs must be paid before the action is added to the chain, but it doesn't define cost to the best part of my knowledge.

This is one of those things where they expect common sense to do the work for them. A cost, as it states in the rulebook must be paid at the triggering of an effect, along with any targeting, all choices, and meet any requirements in order for it to be triggered. Those two resources are spent no matter what happens to its effect.

All costs can be discovered because the cards will use a format that boils down to "do X to do Y." "X" may be paying resorces, corrupting a unit, damaging a unit or zone, sacrificing a unit, removing damage from a unit or zone, returning a card to hand, destroying a development, restoring a unit, etc. Sometimes the cost itself can seem beneficial, but that makes it no less a cost, it must still be paid, and it must be paid by cards you control.