I completed The Black Star quest and found a black soul gem along the way. From what I understand, the Black Star can be used to recharge weapons? The black soul gem can capture human souls such as bandits, forsworn, etc so black soul gems make better enchantments than grand soul gems? How else do they differ from grand soul gems?

They are only different from an RP standpoint. Grand and Black Soul Gems work the same.

Also, try to avoid recharging weapons with Grand/Black Soul Gems. They are better saved for Enchanting. Just use like 4-5 Petty Soul Gems to recharge weapons, or fewer of the higher tiered ones, but save the Grand/Black for the Enchants.

Edited for spelling.

Grand soulgems are used to capture creatures souls. Black Soulgems capture people's souls.

Not sure how it's viewed in Skyrim, but in Oblivion, the black variant were heavily aligned with Necromancers and are pretty much an evil thing to use. Other than the RP flavor and what they capture, they're pretty much the same thing.

Use http://www.uesp.net/wiki/Skyrim:Souls to tell you what 'creatures' have what kinds of souls - some are counter-intuitive.

Black soul gems are beastly finds because you can go to any common bandit hideout and kill the unlucky bastard on guard duty and trap a grand soul that easily.

With grand soul gems, you need to take down Mammoths and all that.

Also, buckom had the besy advice you can get. Recharging weapons with grand souls is a crime, as they make the best enchantments. Get good at that and you can make some really powerful gear.

Yeah, definitely hoard your filled Grand soul gems for enchantments.

The Black Star will hold any soul--it doesn't have to be a Grand one. I'd use it to recharge weapons if it has a smaller soul in it, but if it's got a Grand soul I'd use it to enchant something.

It's funny: you can find empty Grand soul gems very easily, but you have to look a bit to find Grand souls to fill them. Black soul gems are much more rare, but NPCs to fill them are everywhere! That's the reason that most people get The Black Star if it's not contrary to their roleplay: a reusable Black soul gem is invaluable.

A very nice tool to use is to get 100 enchanting, get the last perk that lets you put two enchantments on one item, then enchant a sword with the Fire+Soul trap enchantment then another damage-based enchantment and use the Black Star as well.

Essentially the same as Umbra was in Oblivion, but requires a lot of hard work rather than being able to get it first thing you do. Absolutely wreck people with your amazing sword, and have a reusable soul gem to constantly keep it charged up and powerful.