Enchantment effects are gained by disenchanting items at an Enchanting Altar.

Beware: if you soul trap a Skeever and only have an empty Grand soul gem, you'll trap that petty soul in the valuable Grand soul gem! If a creature dies while Soul Trap is affecting them, and you have a large enough gem, you will capture their soul. You can get it three ways: first, an enchanted weapon with soul trap on it second, the Soul Trap spell in the Conjuration school third, the perk in Conjuration that makes Bound Weapons cast Soul Trap.

Soul Trap is the spell that captures souls.

They're granted to you by completing the Daedric Prince Azura's quest, and you can choose to either gain Azura's Star, a reusable Grand soul gem, or the Black Star, a reusable Black soul gem. For example, a Grand gem containing a Greater soul shows up as 'Grand Soul Gem (Greater).'

Souls display in your inventory with the size following the gem name.

Black soul gems can capture NPC souls but cannot capture creature souls.

Human (and elf and argonian and khajit) souls cannot be trapped save by the sixth type of soul gem, the Black Soul Gem.

Creatures with Common souls can be captured in Common, Greater, and Grand gems, but not Petty or Lesser. For example, Skeevers have Petty souls and can be captured in any soul gem (except Black, see below). Each soul gem can capture the soul of any creature with a soul of it's size or smaller.

Soul gems come in five standard sizes (here in ascending order): petty, lesser, common, greater, and grand.

Skyrim creatures with grand souls