If my father died without a Will and did not list beneficiaries, what do we have to do to gain access to his bank accounts?

Colorado has several ways for heirs to work through a deceased's estate.  If the total value of your father's estate (cars, bank account, personal property, etc.) is less than $50,000.00, then one of the heirs can fill out an affidavit called an Affidavit for Collection of Personal Property.  Essentially the heir swears before a notary that they are an heir, that they are entitled to the proceeds of the account, and that they will distribute funds consistent with the intestate laws.  (Usually that the proceeds will be divided equally amount the heirs).   This is an informal way to resolve and administer his estate.

If the value of his estate and accounts are in excess of $50,000, then you will have to file a probate proceeding and have someone named as an executor of the estate.  This person is usually granted access to the account and authorized to distribute funds. 

If you can afford an attorney, then look for what is called a "probate attorney".  This type of attorney is more experienced in the type of law that is reflected in your question.