Non-US citizens cannot be shareholders in an S corp, so this limits your taxable business entity choices. Mostly, non-US residents will choose between LLCs and corporations taxed as C-corps.
If you form a corporation in Delaware, your corporation will be taxed as like any other US corporation. The corporation will pay the same taxes that any other US corporation would on all US-sourced income and your Delaware corporation would also be taxed on all foreign earnings, in accordance with US Treasury regulations. Since the corporation was formed in the United States, it is taxed as a domestic corporation and you will file Form 1120.
As a non-US resident, your Delaware LLC will only be taxed in the US on income from US sources, meaning that income from other countries will not be taxed by the US. If you choose to form an LLC, any profits US-sourced income will be taxed by 30%. This 30% goes to the IRS. At the end of the year, you will file your US taxes on Form 1040-NR with the actual amount due. If the amount due is less than the 30% initially taxed, the IRS will issue a refund in the amount overpaid. To make sure the LLC is sending the proper amount to the IRS, the LLC must designate a tax withholding agent to calculate the proper amount that must be sent to the IRS before any of the money is released. Because of these difficulties, many non-US residents choose to form corporations, unless they are forming the LLC to do business strictly outside of the US, in which case, the LLC would not owe any US taxes.