I have Flame Atronach spell but this doesn't work because I appear not to have the Apprentice level of Conjuration. How do I raise Conjuration quickly ?

Well withoug glitching your game up, I'd suggest casting bound sword and using it to kill stuff. You can kill the mud crabs and wolves if you wander around rivers pretty quickly. Cast the sword and put it away after you kill one. YOu could even cast and put it away and recast during the same fight if you want to also raise block and armor a bit as you do it.



You have a scroll or the spell?

If you have the actual spell in your magic, perhaps you just don't have enough magika to cast?

Obtain the soul trap spell and continually cast it on a dead body.

Overusing this exploit may unbalance it a bit for you.

You just need the required magica of the spell cost, not necessarily the "apprentice casting perk" if that is what you are concerned about.

As for raising the conjuration skill, you must use the conjuration spells while in combat. So bound sword- as above will raise the skill if you cast the spell as combat begins, or recast it over and over. Summoning during combat has the same effect. Or you can get soul trap and use that on a corpse.

edit: Ninja'd