See guides and lists of common pitfalls for foreigners to set up firms in the U.S.: What Non-Residents Need to Consider When Forming a Company in the US and Starting your own US Company as a Foreigner. Foreigners wanting to start a business of any type in the U.S. follow the same procedure required for the US resident. US residency (or citizenship) are not necessary to incorporate in the US. However, non-residents may run into problems in setting up a U.S. business because of visas, or because of opening up a U.S. Bank account.

Visas In order to work in the United States foreigners need to obtain a US work permit. There is no such thing as a state visa - the system is centralized and US visa types are set by teh federal government. The US Citizens and Immigration Services provides resources and information on visa requirements and processes for working in the United States. The USA has roughly six different types of visas:

• Immigrant (permanent, employer-sponsored workers)
• Family (fiancés, family of current U.S. citizens and green card-holders, family of refugees)
• Humanitarian (refugees and asylum seekers, victims of trafficking, battered spouses and children, etc.)
• Adoption (children adopted overseas and brought into the US)
• Military (citizenship for military members and their dependents)
• Temporary workers (specialized, time-limited professions, athletes, actors, etc.)

Opening a Bank Account You should open a U.S. bank account for your business before you start your business. However, it has recently become somewhat difficult for foreigners to open a U.S. Bank Account. This source recommends three possible ways to get a U.S. bank account.

• “Get a visitor visa, travel to the U.S., go to your bank of choice, and personally open an account.
• Go to a U.S. bank with a local branch in your country of origin for identity verification, if their policies allow such an arrangement.
• Use third-party services to help you set up an account.”

Also note other small differences for foreigners setting up firms in the U.S., taken from this guide:

• A foreign citizen may be a corporate officer and/or director, but may not work in the United States or receive a salary or compensation for services provided in the United States unless the foreign citizen has a work permit. If forming a new company, the foreign citizen would need to also obtain a separate work permit to work for the new company.
• Under US tax law, a nonresident alien may own shares in a C corporation, but may not own any shares in an S corporation.
• Foreign citizens will face a slight delay (~30 days) when applying for the EIN (Federal Tax ID).
• You don’t need a US address to incorporate in a US, but you do need a US mailing address through some provider.

Sources

• What a Non-Resident Needs to Consider when Forming a Company
• US Citizenship and Immigration Services
• Starting your own US Company as a Foreigner
• How to Start a Business as a Foreigner