Children of slave mothers were slaves, and children of free mothers were free regardless of the status of the father.

Inherited lifetime slavery was the norm.
Manumission--granting freedom--was infrequent in British North America.
Occasionally, masters who had fathered slave children would later give them their freedom.

A few other slaves were able to purchase their own freedom although, strictly speaking, this was a legal impossibility.

The slave was not able to own property according to the law, and this meant that the money with which he purchased his freedom had always belonged to his master.

Obviously, he could only do this with his master's fullest cooperation.
In South America, however, manumission was much more frequent.