I'm about 50 hours into the game and not really understanding soul gems. All I know really is that you can use them to enchant your weapons. I've used a couple of "Grand Soul Gems" on a couple of weapons that I have but they seem to run out pretty quickly.

I'm also not really understanding the "capture the enemies soul" upon death. I have a weapon that says if I kill an enemy within 4 seconds I capture there soul into an empty gem. Not really sure where I can find empty soul gems to fill it up with there souls.

So I'm pretty lost.

Basically it's like this, whenever you kill an enemy will the soul tap weapon, their soul goes into a soul gem, which if you have any empty will get filled up, you can then use those to fill up enchantments or enchant new items.

Also a tip, whenever you fill up an enchantment the enchantment bar will go grey, try to use the lowest value soul gem that will fill it up the most.

Soul gems are items that are lying about in caves/dungeons etc, they are also for sale at various shops and magic users (college)

There are different levels of soul gems Petty being the lowest and Grand/Black being the highest.

Each living/undead being in skyrim has a soul that can be captured and each soul have a value (the higher the being the larger the soul value.)

The soul gems once filled can be used to fill up a depleted enchanted weapon, or create a new enchanted item.

Have a look on Wiki for more detailed instructions.

You'll eventually find tons of soul gems just from random adventuring through dungeons/caves/etc. I think you can also buy them from vendors that specialize in magical merchandise.

If you're using a weapon with soul trap, make sure it gets the killing blow and you have a soul gem available that's suited for the "size" of the soul you're capturing. I'm not sure of specifics, but souls have different "sizes" depending on the type (small animal souls are tiny, versus human souls), so you can trap a petty soul in a Grand Soul Gem, but you can't trap a grand soul in a Petty Soul Gem.