[person] + 来
[person] + 来 + [verb phrase]
来 + [number] + [measure word] + [noun]
来 can stand in for whatever verb the situation calls for. Its most common job is volunteering: 我来 means "I'll do it", 你来 means "your turn".
Before another verb, 来 says the person is stepping in to do it. It doesn't mean coming anywhere.
来 + quantity + noun orders food or drink: "give me…". 再来 asks for another, or for something again.
来 comes before the verb it stands for, not after it.
A learner hearing 我来做饭 sometimes reads it as "I come to cook". The person is already there; 来 is the volunteering.