How does an heir go about claiming a bank account?

Was there an estate proceeding opened for your Father at the time of his death?  Was this an account that was missed?  Have you contacted the bank to see of the account still exists or if it went to the State as unclaimed property?

Depending on the amount and the answer to the questions above I would contact the banking institution and see what they need. Some banks want a copy of Letters Testamentary - those given the personal representative of an estate - before they release the funds.  It also matters if the account was in your Father's name also and the the payment may only be allowed to go to his estate, and not you directly, unless you can prove you are the only heir.  Thre are many little things here that can come in to play, such as estate taxes, estate debts that should have been paid, etc. and it is difficult to answer this question without knowing all the information surrounding your Father and his general estate.  Once you have all the information from the banking institution seek legal help.