If you're trying to level it through summoning creatures or weapons, you need to be in combat or near hostile NPCs to level it, also conjuring equipment tends to be slowish for leveling conjuration from memory.
Fastest way I know of is to Soul Trap a corpse repeatedly.
If your game is bugged you can try using a trainer or a book to force a level up, which should reset some values that may be causing it.
Yeah, the Soul Trap corpse method, I believe is the quickest and no hassle way to level Conjuration. It's a very long and arduous process. It's also good since you only have to Soul Trap a corpse, and you won't have to be in combat. Combat reduces Magicka regen drastically.
Yes. If the OP hasn't already, be sure to unlock the "Apprentice Conjuration" perk in the Conjuration tree. It'll cut down the magicka cost for Soul trapping by half. And whatever enchanted items you have that reduce the magic cost for casting Conjuration spells, be sure to wear them too.
Also, if you have not already, you can try doing the side-quest for Drevis Neloren. The side quest which involves purifying the focal points in and around the college using the Mystic Gloves. But in order to receive the desired effects, (Limitless Magicka Regen), you'll have to be a fairly high Character level. Say, over level 28+. Any lower, and you might just get some soul gems.
If all goes well, and you do this quest a high level, like I've already said, you character will temporarily experience near unlimited magicka. It'll last for two real life hours, which is more than enough time level up Conjuration to 100.
The fastest way I've done it was to be a High Elf to use the Highborn power (much faster magica regen for 60 seconds), have mage robes (Adept or Apprentice are the best you'll be able to find at low level), the Mage Stone active for 20% faster leveling of Mage-type attacks, and a combination of a Banish spell with a Flame Atronach or Familiar (not Flaming Familiar, which needs a very high-level spell to banish the creature) to summon the creature in one hand, and a Banish spell in the other to banish the creature as soon as its summoned. Can be used to level up Conjuration quickly, even out of combat. One can also, instead of finding both spells, just get your hands on the Soul Trap spell, kill an enemy (doesn't matter how powerful, but Dragons won't work, for obvious reasons) and then stand over their corpse and repeatedly cast Soul Trap at the dead enemy. Works even faster if both the Mage Stone is used and Lover's Comfort (from being married and sleeping in the spouse's house) or Well Rested from sleeping in your own bed.