Alright I feel like an idiot but how do I do it? Can't seem to find a way to do it on the fly, hoping I'm just missing something.

Enchantment table? I Think

One of the options in the menu describes in detail how to do everything in the game.

Press T on a weapon in the inventory, then have fun scrolling through all of the soul gems you have.

I just found out, never mind.

For those who stumble here looking for an answer, you go to the weapon you want to recharge, then press RB (on the 360) and choose which gem to use.

Go into your inventory, highlight the item, and it will have an option to recharge it if you have a filled soul gem - 'T' I think on PC.

So I can assume it's R1 for the PS3.

PC - T

Xbox 360 - RB

PS3 - R1