Hiring the best talent without prejudice sometimes mean you will want to hire someone who is not a U.S. Citizen or permanent resident. How do you do this?
First and foremost, you should work with a legal counsel who specializes in immigration law. This is because immigration law changes frequently, and what your mentors might know from their personal experience is frequently out of date and therefore inaccurate. Working with legal counsel makes sure you are doing the right thing for both the candidate, your company, and the U.S. population.
Secondly, you can read up on the current rules and regulations on websites maintained by the U.S. government. In particular, the website for the U.S. Citizen and Immigration Services (formerly Immigration and Naturalization Services) is the definitive resource where you can look up information about visas that allow foreign nationals to legally work in the U.S. You can look at other websites too, but the USCIS site is the single source of the (changing) truth, and this is one area where you want to make sure what you know is current.
Lastly, there are various efforts to help foreign born nationals to stay in the U.S. and contribute their talents to the workforce. The state of Massachusetts in particular has been pioneering a number of new ideas, such as the Global Entrepreneurship In Residence program proposed by Gov. Deval Patrick in 2014 which is currently being piloted at the University of Massachusetts.
Again, the best bet for you to understand your options is to work with an immigration attorney who will be able to advice you on the latest rules and regulations you need to comply with as an employer hiring non-US citizens and non-US permanent residents.