i'm completing the mission of retrieving the horn from Ustengrav. There is an enchanter there. I have a weapon, a soul gem, but don't have an enchantment. So, where can I can I get the enchantment to use the enchanter in Ustengrav to recharge my weapon?

You can just press T ( if you're on the xbox/ps3 I have no idea) in your inventory, and you can choose a (filled) soul gem to charge your weapon. No enchanters needed.

you must disenchant a weapon to learn its enchantment
to recharge a weapon you go into your inventory, highlight it, and press R2

I don't fully understand your question.

If you have an enchanted weapon (example: Steel Sword of Fire ) and you want to recharge it you need to look at it in your inventory and press the RB button (Xbox) and select a soul gem to use.

If you want to enchant a weapon with for example Fire Damage, you must first use the enchanting table to Disenchant an enchanted weapon which destroys the item.

Next you select the item you want then the enchantment then the soul gem and press X to craft it.

Talk to the court wizard in Whiterun, he'll explain everything.

Disenchant any already enchanted items you have, then you have the enchantment.

If you have a low enchanting skill, the enchantments might be pretty useless. I usually power level it on some useless items of mine.