ok LISTEN, neither of these people answered the question

you have to cast Soul trap on a creature (either by knowing the spell, using a scroll, or using a item enchanted with the spell, i like to make a weapon enchanted with soultrap so that i don't have to cast it all the time)

when the spell is cast there will be a white cloud around the creature

if you have an empty soul gem in your inventory, and it is big enough (stronger creatures require larger soulgems) and you manage to kill the creature before the spell wears off,

then you now have a full soulgem which can be used to either:

#1 enchant an item

#2 recharge a magical item that has run low on charge (i think this is useless because magic items recharge by themselves over time, so this just wastes soulgems)

Quote: rock n rat

how do u get a soul in a soul gem?? and how do u enchant things like swords??

once you have the soul gem (with the soul) you simply equip it to your character. the 2 buttons will appear and they will say: 1 recharge encanted item or 2 make enchanted item the rest is hard to explain but easy to do.

You have to cast a spell over the creature with the soul you want to trap. It does not work on humunoids. You can either learn the spell, buy a scroll with the spell, or find an item that has this enchantment. I personally think that you shouldn't try this until later in the game. It can get costly.

you gotta kill a monster and then put the soulgem (in inventory) on your picture and you can enchant but you need decent skill first