1. NYS does not provide or approve your curriculum.
2. You are required to teach specific subjects. The content and how your children learn is completely up to you.
3. Homeschooling does not need to look anything like school; in fact, it usually works best when it looks little to nothing like school.
4. Schools are set up so that a single teacher can assess the knowledge of 20-30 children (s)he doesn't have a deep personal relationship with. Homeschooling can be relationship based where things like casual conversation or telling Grandma what you learned can replace worksheets and tests. You know what your kids know because you know your kids - just like you knew when they were crawling, walking talking, etc. And just like they didn't need formal "how to go potty" lessons, kids at home often learn with no formal lessons and a lot of real-life involvement. If we all sent our kids to school to learn to use the potty, in a generation we'd question if they could learn without a worksheet. Can you picture it? Pick up the picture that shows the first thing you do when you go potty (child picks up picture of pulling drawers down). If this sounds super stupid it's because we've not been programmed to think kids need "school" methods to learn before age 5. Why do they suddenly need them at age 5?
5. NYS requires a Letter of Intent or LOI, an Individualized Home Instruction Plan or IHIP (pronounced eye-hip), 4 quarterly reports, and an annual assessment. They also require that your child is learning for a specific number of hours. Nobody counts those hours; we simply put that the hours were met - since learning at home occurs round the clock and on weekends and holidays too. These all go to your local school superintendent's office unless they contract out to BOCES. Ask around and people will tell you who your local point of contact is.
6. NYS does not approve your curriculum!! Some school districts don't understand this. They are only allowed to make sure you are following the regs - covering each required subject in some way and listing some sort of curricular resource for each subject.
The Nitty Gritty
LOI - First - you send in your letter of intent or LOI which states name, age, grade, and that you will homeschool. Sign and date it. This is due whenever you decide to homeschool.
IHIP - Next, you send in an Individualized Home Instruction Plan or IHIP (pronounced eye-hip) that details the annual plan. Regs tell you when this has to be in; it's due so many days after your LOI.
This can be very simple. List each required subjects. Write a sentence about what topics you will begin with or the overall goal or plan for that subject; don't be too detailed. Be sure to say "Other topics will be covered as opportunities and resources dictate". Then write "curricular resources will include but not be limited to the following" and list some resources for that subject.
Those particular ways of wording things above allow you the flexibility to adjust your plan at any point in time during the year. So, if your child, for example, is suddenly obsessed with opossums and wants to learn everything there is to know about them, you can ditch what you had planned for science next and simply report a sentence or so about oppossum zoology in your quarterly reports for science and include a sentence about research in the English Language Arts (ELA) section. Without the specific wording, you are locked into adhering to your plan or reporting changes.
About curricular resources - I always list a specific reference book or reference curriculum, plus videos, podcasts, YouTube videos, games, apps, field trips and things like that for curricular resources. While the book I list includes an actual title and author, I literally write "YouTube videos, podcasts, community professionals..." for the rest. Leaving it vague allows us freedom to uncover and use resources along the way. By the way... starting with things you know your kid is really into (dinosaurs for science or cooking for math) and asking kids what they want to learn about can be REALLY fun!
Repeat the sentence or two summary and curricular resources for each subject. Put your child's name/grade and the date on it. Add your quarterly report dates (more below). Now you have an IHIP. (Note: Many people combine English Language Arts (ELA) into one subject; just be sure to touch on each required aspect.) That wasn't so difficult right?
Quarterly reports - Think of these like report cards. Pick 4 dates about evenly spread out. For each one, you'll send in a sheet that lists each subject and includes a couple bullet points of what has been covered. State at top of the sheet that you covered the required hours and the child made satisfactory progress in all subjects. Again, less is more. The schools don't need tons of detail. They only need to hear from you that you've met the regs.
Annual assessment - You turn this in with your 4th quarterly. There are two kinds of assessments - narrative and testing.
Narrative assessments can be done in grades 1-3 and biannually in grades 4-8. For a narrative assessment, state that your child met or exceeded all expectations as set out in the x grade IHIP and will proceed onto the next grade. Sign. Date. Some folks add "highlights of the year included learning cursive" or something similar for most subjects. I never have. A few districts will tell you that you can't write your own narrative. When I moved to my current district, I had to have a certified NYS teacher I know sign off on it. Other times, parents make a peer-review-committee and sign off on each other's narrative assessments. Both are discussed in the regs below.
A testing assessment is required in alternate grades for 4th-8th (so 4, 6, and 8 or 5 and 7). They are also required annually in high school. Most folks do the California Achievement Test (CAT) or the PASS test - both of which test basic math and ELA, like very basic. You are not required to do NYS common core testing or to test all subjects. Your child must have a cumulative score of 33rd percentile or greater meaning that they can pass if 67% (100-33 = 67) of the kids the test was normed on scored higher than them. In other words, don't sweat the tests.
Below is the link for the much more complicated and verbose NYS regs. They're helpful to let you know required hours (nobody counts them bc learning happens all the time at home) and what subjects you have to cover when.
I hope that provides a concise and non-scary summary for you! <3 You might not have chosen to homeschool if not for the pandemic, but this can be a super exciting and bonding experience over the joy of learning if you think outside of the school-at-home box.