My sister passed away June, 2023. I have an "Inherited IRA" opened with my brokerage. I want to take the RMD 10-Year method. how I declare that to the IRS?

Yes, exactly.  

If you are less than 10 years difference in age from your sister, you might be an eligible designated beneficiary, which gives you an additional option of withdrawing the payments over the remainder of your life expectancy.

If you are not an eligible designated beneficiary, or you don't want to follow that set of rules, you can follow the "10 year rule" which is the same for everyone else.  The 10 year rule has two parts.

1. You must withdraw at least your RMD each year (you can always choose to withdraw more).

2. You must withdraw all the money and close the account by December 31 of the 10th year, in your case 12/31/2033.

For RMDs, if your sister was past her beginning age and did not take her RMD in 2023, you must take the RMD for 2023 based on her life expectancy table.  Then starting in 2024, you take your RMD based on your life expectancy.  You can always withdraw more, if you choose, and you can close the account in less than 10 years if you want.  You may want to think about the tax impact of spreading the withdrawals out more evenly, or taking the minimum and then a big withdrawal at the end -- it will depend on your age, other income, and tax bracket.

You don't need to officially "declare" anything to the IRS.  Just start following the 10 year rule.