How do I file my taxes and claim my kids when I have had no income

You don't. Your exemptions go against income. No income = no exemptions.

Is that your question?

JudyKayTree is correct; no income = no tax return.

However, assuming you are either getting child support from the father or you are living with someone who is supporting you, you AND your children MAY be able to be claimed as dependent by either the children's father or by whomever is supporting you.