Lucius the Eternal

To trap a soul, you must either have soultrap spell or scroll or magical item with the effect 'Soultrap'. Once this is done, use it on a monster and kill it. Providing you have a soul gem of high enough quality, it should work. At first simply use petty and lesser gems and practice on rats, cliff racers and the likes. If you succeeded, there will be a notification saying you have trapped a soul. For large or more powerful enemies, such as the winged twilight or dremora, you will need bigger gems. If you plan to trap a large soul such as an atronach or anythung that is strong, make sure you have a high quality gem, such as grand or greater gems.

I hope that this has helped.