There is not one universally way of selection, however in an ideal world, the project manager has access to a potential pool of candidates and interviews them. I would look for experience and skills specific to the project work that needs to be completed first, especially for knowledge based work (e.g. computer application development, IT).
Next, I would look for resources that demonstrate flexibility, dedication, leadership, and loyalty to their work. If they don't have all the skills or are unable to get along with the team, they will at least adapt and be full contributors.
Finally, I would look for interpersonal skills to get along with the rest of the team. Too many start here and end up with nice people that cannot effectively complete the work at hand. Its important, but I would value skills and experience over interpersonal attributes.
Just my opinion! Any other ideas?