I dont actually set this up. I go through an introducer.
depending on which bank you need various things. the less you have the more expensive and really its a case by case thing depending on which bank you go to.
Costs go from personal 1,500 USD to Corporate 2500-3500 depending on certain factors, and an offshore company with US bank account about 5000 USD.
Most need two forms of ID, address in the states for receipt (extra cost if you dont have), and possibly a bank reference for certain banks, and for a foreign company the list is a lot larger.