Enter the new 40k Magic phase. It appears that Games Workshop have taken 8 editions of knowledge and experience and adapted the solid Fantasy Magic phase for 40k. With each power having a casting value (1, 2, or 3) required to cast, and dice generated by rolling a D6 and adding the number of mastery levels in your army to the total.
From what is known, you are required to roll a number of 4+'s equal to or greater than the casting value of each power. This is a small deviation from WHFB and may just be a strong indication of what we will see when 7tth edition lands (rumoured to be September this year).
Dispelling is done similarly to casting but require 6+ to be rolled on each dice, and the number of 6+'s must be equal to or greater than the 4+'s rolled to cast it. There are rumoured modifiers to these rolls like psychic hoods etc that give +1 for the rolls.
It appears the similarities between the two systems are ever increasing. Can't complain, the mechanics of WHFB have always been superior, and moving 40k closer to them can only improve the game.