You can claim a child on your 2010 tax return if the child is born before or on Dec 31, 2010. As far as claiming the child on your W-2, when filling out your W-4 for your employer list the child as a dependent in order to receive the credit throughout the work year. If you have not already claimed the child at work then request a new W-4 in order to update your information.
This information is based on the limited information you have provided. Children of divorce, guardianship or extended relations may fall under different rules based on circumstances.