One very important step five to add: check with your state's Secretary of State office to see if there are any additional steps that must be taken. Many states require foreign-registered LLCs and corporations to submit an "application for authority to transact" or otherwise register with them.
Depending on where you're located, a local business registration fee or license may be required as well.
It's also important to apply for an EIN number, which is generally required before opening a bank account in the business' name, and for tax purposes: https://sa2.www4.irs.gov/modiein/individual/index.jsp
There may be other steps that I'm missing, but as with any guide to navigating these waters, always ask for help in your particular situation, and don't be afraid to (indeed, please do!) consult a lawyer.