like in 履いてきた靴
how would it change if i wrote 履いた靴?
This (-て)くる is a subsidiary verb explained in this question:
The difference between 履く and 履いてくる is almost the same as that between 持つ ("to pick up; to hold") and 持ってくる ("to bring"). 履く only refers to the action of wearing shoes, but 履いてくる is used when someone came to somewhere wearing the shoes (thus effectively "bringing" them). 履いてきた靴 refers to the shoes someone was wearing while they were coming.