If you cast a spell, you cast the first stage, or the opener. If you cast a spell again, you cast the second stage, or the flow. If you cast again, you cast the third stage, or the finisher. You can mix the spells you cast, but the stage you're on will always be constant.
Say for example you cast her first ability, Barrage. It'll be the Opener so you'll fire off 12 ice projectiles, and after you are done you'll be in the second stage Flow. From there you can cast barrage again to shoot 6 fire projectiles, or her second ability, Asaara's Leap for the flow stage, where you leap backwards for electricity. From there you'll be in Finishing stage, and again can cast the spells for their stated finishing effects.
Note that the stages all have a time limit, which if you do not cast a spell in the time, will revert you back to opening stage. Sorry if I wasn't clear, because I'm awful at explaining things.