First, if your father was older than his RMD beginning age, and did not take his RMD for 2023, you have to take that for him, based on his statistical life expectancy according to the tables in publication 590-B. (But remember, an RMD is just an amount, not a specific transaction. So if we assume his RMD was $5000, that could be satisfied by withdrawing $5000 all at once, but it would also have been satisfied by withdrawing $450 per month over 12 months.)
If your father was not older than his RMD beginning age, you do not have to take RMDs at all, you just have to empty the accounts by the end of the 10th year after his death (Dec 31, 2033).
If your father was older than his RMD beginning age, then you must take RMDs based on your age starting in 2024. Or rather, you base your RMD on your life expectancy. Suppose your life expectancy this year is 30 years. Your RMD is 1/30 (3.33%) of the IRA balance. There are several life expectancy tables in IRS publication 590-B, and I don't know which table you should use, because the IRS has only just finalized these regulations and the publication is not updated yet. But @dmertz will know which table to use.
https://www.irs.gov/publications/p590b#en_US_2023_publink100090423
If you must take his RMD for 2023 now (late, in 2024), you have report the missed RMD on your 2023 tax return. There is a penalty but you can request a waiver, it is almost always granted. Then you still need to also take your own RMD in 2024.
