Sorry to hear about your loss.
I had to organise a funeral and wind up an estate last year so I have some insight into what you're going through. In terms of specific red tape to my knowledge you shouldn't have too much to deal with. It's more a matter of organisation. If I might weigh in with a few bits of advice:
First of all, act quickly. I know it probably feels a little overwhelming right now but things are easier to deal with if you get on top of them sooner and once you're done it will be a weight off of your mind and will give you some peace to grieve.
Next will want to make a list of any people or organisations your father had arrangements with, this could be bills, accounts, even newsletters etc. The best place to start is his Bank Statements, get at least 12 months worth (preferably 24) and make a list of anyone he was making regular payments to or who he was receiving regular payments from. If he had multiple accounts do this for each. Keep any letters etc which arrive for him and add the senders to the list. Finally add any public bodies to the list, government (local and federal), DMV, etc.
Now you have the list divide it up.
Start with the banks and have them freeze the accounts (as long as they are not joint accounts with his spouse/partner). Then contact anyone he was making payments to and inform them of his passing. Most contracts etc automatically terminate on death but if anyone disputes this or claims there is an outstanding debt, make a note but don't pay anything and whatever you do, don't indicate that you will accept liability for the contact/debt yourself as any debt will need to be settled by the estate. If your father does have a spouse/partner then it would be prudent to have bills such as utilities turned over into their name to ensure they don't get cut off.
If your father was receiving any income (say from a pension) then they should be contacted next. It sounds mercenary but it is always worth asking if there is a death benefit attached and asking for a copy of any policy documents or the like to check for yourself - a lot of money goes unclaimed in these exact circumstances. If there are any death benefits or assets to be transferred these will usually form part of the estate so make a note of who owes the estate what.
The rest of your list will mostly just be FYI phonecalls. These might seem pointless but it is less work in the long run and means you won't have the upset of receiving a jury duty summons for your father six months from now.
Finally you need to wrap up the estate. If you have a lawyer handling all of this then turn any information you have collected from the above about money owed or outstanding debts over to them and leave them to it. If not then you have some work to do and I would advise taking some advice from someone who better knows your legal system but here is a basic outline:
Get written confirmation from everyone of any money they owe the estate and any claim they have upon it. Then add up the value of any assets (bank balances, value of his house if he owned it, any stocks or bonds he might hold etc.)
Call in any money owed to the estate first. Ideally speak to your bank, have a dedicated account set up for the money to be paid into and into which you can place the proceeds of any assets you have to sell.
Once this is in and you know the worth of the estate then you need to pay any debts. Make sure you get confirmation in writing of these and do take advice on whether they are valid claims as not all debts are enforceable after death in all jurisdictions (most commonly gambling debts and the like are unenforceable after death, but it varies). If these debts can be settled from liquid assets (cash) then do so. If not you will need to start selling assets of the estate to pay the costs. If specific assets have been bequeathed to certain people in your father's will then these can't be sold to pay off debts unless the debts can't be covered by selling assets that weren't left to specific people.
If the total value of the estate is exceeded by the total debts then everything will need to be sold. Once this has been done there is a pecking order of who gets paid. Unpaid tax usually comes first (first Federal, then state, then local). If you still have money after this then any outstanding mortgage or secured debt (loan borrowed against a specific asset) comes next. After these have been paid in full then unsecured creditors get paid (unsecured bankloans, unpaid bills, private debts). At any stage if the bill cannot be paid in full and there are multiple creditors with an equal place in the pecking order then the money is usually divided in proportion to the debt. For example if you have two bills to pay of £800 and £200 but you only have £500 to pay, then they would receive £400 and £100 respectively.
If the debts have been paid and you have money/assets left then you will need to distribute them. There may be death taxes to pay here so check that first. Then, if you father left specific legacies in his will (assuming he made one) these need to be distributed first - for example if he left £2000 to a charity. Then everything that is left after this goes to the residuary beneficiaries. If he had a will it will state who these are any in what proportion they will receive this, if not then it will depend on his circumstances. If he is survived by a spouse then everything will go to them, if not then it will usually be evenly divided among his children.
That is a very rough outline and based on my understanding of US federal law. I would advise checking with a lawyer or someone who understands your state/local law before acting on any of the above.
Be well and I hope things get sorted without too much stress.
