To claim the credit you must meet these tests, to qualify for the credit:
The dependent must be a U.S. citizen or resident, and a blood or adoptive son, daughter, stepchild, or grandchild. Foster children qualify if they lived with you as members of your household for all of 2010.
You must report each qualifying child's tax identification number (usually the child's Social Security number) on your return for the year that you take the credit.
You can read more about it at the IRS website and they will do your taxes for free if you meet certain guidelines.
Again here are the guidelines for claiming the Child Tax Credit:
Amount - With the Child Tax Credit, you may be able to reduce your federal income tax by up to $1,000 for each qualifying child under the age of 17.
Qualification - A qualifying child for this credit is someone who meets the qualifying criteria of six tests: age, relationship, support, dependent, citizenship, and residence.
Age Test - To qualify, a child must have been under age 17 – age 16 or younger – at the end of 2010.
Relationship Test - To claim a child for purposes of the Child Tax Credit, they must either be your son, daughter, stepchild, foster child, brother, sister, stepbrother, stepsister or a descendant of any of these individuals, which includes your grandchild, niece or nephew. An adopted child is always treated as your own child. An adopted child includes a child lawfully placed with you for legal adoption.
Support Test - In order to claim a child for this credit, the child must not have provided more than half of their own support.
Dependent Test - You must claim the child as a dependent on your federal tax return.
Citizenship Test - To meet the citizenship test, the child must be a U.S. citizen, U.S. national, or U.S. resident alien.
Residence Test - The child must have lived with you for more than half of 2010. There are some exceptions to the residence test, which can be found in IRS Publication 972, Child Tax Credit.
Because of the Relationship requirement, you boyfriend will NOT be able to claim your son. He could if you were married before the end of the year 2010.