Most, if not all, LAUSD schools are now enrolling kindergarten students for the fall. At our local school, you need to pick up the enrollment forms at the office and make an appointment to submit the forms at a later date. The forms include a card that needs to be filled out by your child's pediatrician. To find out which school is your "home" school, click here.
If you are going to enroll your child in before and/or after school care, I highly recommend enrolling your child in kindergarten as soon as possible. Most, if not all, programs require that your child be enrolled at the school before they can be enrolled in the program. Space for before school care is particularly limited.