First, call the school district's main office and ask what paperwork they will need (ie birth certificates, social security cards, utility bill, etc). Then, go up there with the paperwork they have requested along with your proof of temporary custody. They should be able to help you do the rest.
Below are some resources you may find helpful for school enrollment and preparing for Back to School -- including a link to the SchoolFinder directory of U.S. schools (in case you don't have the school's telephone number already handy).
If you don't already have a legal custodial agreement or a caregiver's authorization affidavit, you might follow-up with your lawyer (or search online) to have those documents prepared when you go to the school(s) to enroll the children. I'm including a link below to a California school district that offers such forms on their website for families in their district.