Take out the trim from the perimeter of the floor with a pry bar and hammer. Don't break it.
Fill the cracks in the surface with concrete floor patch, using a trowel to spread it on. Level out any uneven sections of flooring around the cracks by spreading additional patch over the whole area, getting it as flat as possible. Let it set for 24 hours.
Roll out a course of moisture-barrier underlayment along the edge of the floor where you want to start. Cut it to fit with your razor knife.
Set a floorboard alongside the wall at one end, putting spacers between the board and the wall so the board is held 1/2 inch out. Lay a second board off the end of the first one, fitting them tightly together by their ends.
Set additional boards end to end all along the length of the floor, fitting them together in the same manner. Cut the last board in the row on a miter saw to fit at the end.
Spread down more underlayment as needed. Set the second course in place alongside the first course, locking the boards to each other by their long sides. Position the boards so the ends don't line up between courses.
Repeat the process of laying the courses one by one, working your way across the floor. Cut the last board of each course on the miter saw as needed. Continue to spread down more underlayment as needed.
Cut the boards of the last course along their lengths on a table saw, so they fit along the last wall with a 1/2-inch space left there.
Reinstall the floor trim around the perimeter using your trim nailer. The trim will cover the spaces by the walls.