It's always possible this will be delayed again, but it looks like it's going to happen this time.
To leave high school with a diploma, next year's graduates need to pass the first California High School Exit Exam administered, not for practice, but for real. See The California Department of Education.
That means they can show they've mastered eighth grade Math and tenth grade English, which you'll probably agree is not a bad thing.
It's scheduled to happen in September, November, February, March, and May. All of those in tenth grade take it once next year. If they pass it, fine. If not, they have five more chances. Eleventh grade students can take it in the Fall and try again in the Spring. Twelfth graders get three tries before they're out: once in the Fall, and twice in the Spring. They're the only students who get a third chance in the same year.
The students who don't pass (and it's anticipated many will not) still get to finish up with their classmates, still participate in the graduation ceremony, still get a rolled-up paper to take home. It's called a Certificate of Completion.
It certifies that the student has satisfactorily completed a prescribed alternative course of study, or (in the case of Special Education students) has met the goals of his/her Individualized Education Program (IEP).
General education students may need help understanding that four-year postsecondary institutions will want the diploma: if they finish with a Certificate of Completion, it may be necessary to go on to one of the local Community Colleges for a General Equivalency Diploma(GED) before applying to them.
Special Education students may need help to recognize that the Certificate of Completion represents an achievement by itself, and is a fine thing. It means, for example, that help for the student and for the family can continue: the school district's Transition Services are available only to those students without a change of placement. A Certificate of Completion allows that; a diploma does not. (In the terms of the law on K-12 education, the school district is finished with a Special Education student with a diploma.)
The whole eastern half of the United States has had standards for high school diplomas for a couple of generations or more. Many western states have had them too. California is belatedly playing catch up, and trying to do that fairly; but for a while, it may be a rocky ride. The press will continue to write about it, but so far none of them has bothered to learn anything, so don't go there if you need information: stay tuned.