If my dad recently passed away without a Will, what do we need to do now?

You don't mention the state where your dad passed away... but most states, including Texas, require an estate to be probated in the county and state where the deceased was residing at the time of their passing.  There may be some exceptions depending on your father's situation... but that is the general rule.
From there, you need to visit with an attorney in the state and county where he passed away so that you will know all of your options for a probate in that state.  In Texas, probate is not automatically required when someone passes away.  If the estate was small and of little value, the balance and remaining details of the estate can be resolved with what are call "affidavits of heirship."  Basically, all of the heirs agree on what can and should be done with the residual of your father's estate.  This is really the cheapest and easiest way to deal with small things. (boats, cars, personal items...)  If the estate is larger or the heirs will not agree on how to proceed, then a probate may be required.  Before you visit with an attorney, it's helpful to make a list of property items (personal, real estate, general) and let the attorney review the list so that they can advise you on what options are best for your situation.  Many heirs like to squabble on minor details... but don't understand that squabbling is usually not cost effective for most estates.  Probate fees can quickly eat up many small estates if the parties do not maintain a proper focus on what is really important, which is honoring the deceased and the life they had.