I want to fill soul gems but i am not exactly sure how to go about doing this.

I have soul trap spell. Do i just cast it then defeat ANY enemy?

Or do i have to defeat larger enemy's?

for normal soulgems you can only fill it with monsters or animals. the stronger the creature the better the soul. soul gems can only hold creature at the the same lvl as them or weaker Example petty soul gem can only hold up to petty lvl souls, grand soul gems hold up to grand