It's not new construction -- it's basically a "used" house if you want to think of it that way. Most homes on the market are resale homes. Although the builders are starting to build again and you might be able to find new homes in your area.
As far as "what's needed" -- same thing as with any house. You need to first talk to a lender to get prequalified for a mortgage (unless you're paying cash). The lender will look at debt to income ratio, credit score, job history, savings, etc. Once you find a house and put a contract on it, it's still the same process as buying new. You'll want to get it inspected, you'll need an appraisal, etc.