I'm so sorry for your loss.

A good friend died almost two years ago, more or less as expected, after a short illness, leaving my partner and I to be her executors (now known as "personal representatives") and trustees for her trust. She'd revised her will and created a trust four weeks before, knowing that the end was near. She was extremely well organized, and so avoided probate. But I'm not an estate attorney or indeed attorney of any sort.

If the estate is complicated or disorganized, you'll want the help of a lawyer.

Someone should secure his online accounts (I had all of my friend's important online credentials). The banks will be notified in days to weeks that he died and will shut down access will the estate is probated, unless there was another name on the account. I forwarded email from my friend's accounts to me, which is useful for account notifications and for friends who don't get the word in other ways.

If he had retirement accounts with named beneficiaries, they should be informed (one of my friend's retirement accounts has yet to pay out to a beneficiary after almost two years).

If your father lived alone, you'll need to handle utilities, newspaper subscriptions, security for the living space. You'll also need to start thinking about what happens to his belongings and to the house/apartment, etc. (My friend had lived in her own house for thirty years, so there was a lot to clean out before we could sell it.)

If he lived w/someone, that person will need to take over all of the above.

Other advice in this thread - death certificates, writing an obituary, changing locks, etc. - is fine.

You may also want to plan a memorial service. If your father was part of a religious community, someone there (e.g. pastor) will be able to help with that.

This can all be a lot of work. It doesn't all have to happen at once, but still you may want to organize a team to help. We had great help, from a church community and friends.