Im trying to enter the Winterhold College. Feralda wants me to summon a Flame Atronach. It's not letting me do this spell. Help?
If you do not have the spell [Faralda] asks of you, she will offer to teach it to you for 30 gold.
Talk to Faralda and choose the appropriate conversation option to buy the 'Conjure Flame Atronach' spell. You should now be able to use it.
Also, from the same UESP article linked above:
Alternatively, you can attempt to persuade her and avoid this test, or if you are here for the quest Elder Knowledge, you can tell her you are Dragonborn after which she will ask to see a shout. Either of these will get you in without needing to cast a spell. In order to persuade her, you will need a Speech skill of 100 (70 with the Persuasion perk) or an Amulet of Articulation, available only by completing the Thieves Guild questline and becoming Guildmaster.