Whats the best way to lay hardwood flooring on concrete?

Are you using real hardwood? Engineered? Glue direct to the concrete. Do NOT put down the plastic barrier. Engineered wood must be glued direct to the concrete. Most important read the manufactures directions and follow them. If you have solid hardwood you have real problems, return and get engineered that can be installed on concrete. If you are using laminate, just lay the plastic on the concrete and lay the laminate on the plastic. If you purchased the lock together hardwood, install like the laminate. MOST important read the directions that came with the floor and follow.

Whether it's engineering/laminate or real hardwood flooring, the first thing you need to do is to make sure that there's not too much residual moisture in the concrete. (Since there was carper on before, it's probably not an issue.)

And if it's real hardwood flooring, you will need to lay down plywood or sleeper boards to nail to.

The link below has some great information and step-by-step instructions.

I wood not use a hardwood on concrete, use a foux laminate, they are free floating and are not effected by moisture unless submerged