How do I recognize correctly the signs of aspergers syndrome for a child?

Asperger. A real good book is called asperger syndrome by tony attwood. You can purchase a copy from amazon, as well as other works by the same author. I highly recommend it. Good luck to you.
Why do you ask? There's no pill to cure it, and it's managed by learning and adapting. The kid who's poor in sports, socially awkward, seems baffled by others, acts like a jerk without meaning to, and has narrowly-focused interests that may seem strange needs guidance rather than a diagnosis. Strength sports over coordination / team sports. Guidance with people-skills. Managed well, Asperger's is a huge plus.
Developmental pedi. Mchatt is not diagnostic but is a screen for communication disorders along the autistic spectrum - asperger's (currently part of the spectrum), autism and pdd-nos (pervasive developmentl disorder, not otherwise specified).A pediatrician specializing in development (board certified) is optimal for determining DX in child with "+" mchatt, & required to get help thru state funding in most states.
Asperger. Asperger can be diagnosed by using the m-chat screening test to see if your child has it. Then referal to specialist to help confirm the diagnosis.
Get an assessment. The only way to get a correct diagnosis is to see a healthcare professional.