During this quest, you'll only be able to sucessfully cast the spells if you've done everything you need to, in the proper order, before you try casting the spells. For example, have you gone around and read each of the pillars? If you do, you won't be able to understand them without going back to Denel and asking him about it. He'll direct you back to Skaleel, who has a reference book.
Get the book form Skaleel and give it to Denel. Speak to him about Translation and you'll find out what each of the four phrases correspond to. Note that he will translate them in a different order from the one in which they are located in the room.
The orginal phrases are:
av molag anyammis
av mafre nagaia
magicka loria
magicka sila
Translated, in order, they are:
From Fire, Life or Fire Damage
Frost Damage
Magicka Darkens or Magicka Wanes or Damage Magicka
Magicka Shines or Magicka Waxes or Fortify Magicka
As you might have guessed from the translation, you have to cast certain spells at the pillar in order to open it (or whatever it does). These spells have to be cast at the pillars - casting Fortify Magicka on yourself won't work. Also, Drain Magicka cannot be substituted for Damage Magicka. The strength of the spells does not matter.
You can choose to use the scrolls in the chest next to Denel to provide you with Fire Damage, Damage Magicka, and Fortify Magicka, but Frost Damage is missing from the chest's scrolls. The scrolls regenerate in the chest after three days if you used them prematurely (you will need to leave Vahtacen for three full days if you want them to regenerate).
As you cast each of the four spells in sequence (Fire Damage, Frost Damage, Damage Magicka, Fortify Magicka), portions of it lower to reveal a stairway. If you make a mistake, you will indeed get zapped by as many of the Dark Welkynd stones that can take aim at you. If you're worried about being zapped, you can stand out by Denel and take aim with your targeted spells from a safe distance.