If I’m a trustee for my dad’s estate and want to do an accounting myself, what do I need to include and what conditions do I have to hold up to?

You have to account for all the changes in trust assets from the start of the accounting period until now; their current form (stocks, bonds, houses, bank account, etc.) and current value.  You need to specify how much was spent and what it was spent for, as well as any gains in value (interest earned, house values gone up, etc.) and you should specify any known but as yet unpaid bills as well.  When you are done, the numbers should balance to the penny and you should (must?) have backup documentation to support every number you list - bills, receipts, cancelled checks, bank statements, brokerage account statements, etc.

You should really consider hiring a professional to do the accounting - it will help protect you from legal claims by your jealous family members; it presumably will be done right and timely; family members may be more willing to take the word of an otherwise un-involved professional than they are to take your word; and the trust pays for the accounting, not you personally except as a reduction in the your share of the total trust's value.  If other family members are going to insist on an accounting, they should have to pay for it as well by reducing their share of the trust's total value, just like all your shares are reduced by the amount of income taxes the trust pays and/or the cost of having the tax returns prepared.   An accurate accounting also helps protect you against future potential claims of mismanagement - if they do not object to the accounting now, they may have trouble doing so at a later date.  All of this protects you and, if something is done incorrectly, you have recourse against the professional accountant whereas if you try to do it yourself but miss something or screw something up, you can be on the hook personally for any losses and it may provide grounds for them to have a court remove you from being the Trustee.  In other words, they may have failed to get rid of you before but if you don't do this right, you may be giving them the ammunition they need to get rid of you now...and you could have to pay for any mistakes out of your own pocket instead of using trust money.  Do it yourself at your own peril.