When you first open a new bank account in the US it will need funding. When you open the account you will typically deposit a little cash to get the account opened. The bank will then give you the new account numbers. Get their routing number also, so you can do wire transfers into the account. This is the easiest way to get large amounts of money from your overseas account, at a reasonable exchange rate, without incurring high transaction costs.
Once your account is funded, you can write or order US dollar checks to pay for most costs. If you have a need to pay small amounts before your account is opened and the person or company doesn't take credit/debit cards, you can use a service such as PayPal or Western Union. Notwithstanding the beforementioned INBIB can advise and assist with these processes.