Given the respective roles of Athene and Hephaistos, it is not surprising that they should be linked. Athene was the goddess of sculptors and handicrafts (hence her role as the challenged goddess in the story of Arakhne), and Hephaistos was the god of smiths. Therefore, they shared an interest in crafts. They shared a temple on the Akropolis (which was dedicated to Poseidon also) - the Erekhtheum.
Of course, Athene was linked with Hephaistos before her birth. When Zeus was in agony due to Athene's impending exit from his head, it was Hephaistos that took the labrys and split his head open.
However, there is another legend, which gives a cause-and-effect relationship between their births. According to this story, Hera gave birth to Hephaistos - who was her own child, with no father. This was supposed to show Zeus that he wasn't the only one who could produce a child without a member of the opposite sex.
The two were were also involved in another way. According to some, Hephaistos fell in love with Athene as soon as she came out of Zeus' head. However, she refused all advances, preferring companionship.
Some say that Poseidon played a part in the following events. They claim that Poseidon informed Hephaistos that Athene was on her way to his smithy, with Zeus' consent, hoping to have love made to her. She was on her way, in fact, to either ask him to make some arms for her, watch them being made or collect them. Hephaistos tried to ravish her, but the goddess resisted. He ejaculated on her thigh above the knee.
In disgust, Athene wiped the semen off with a piece of cloth and threw it down on Gaia (the earth), who immediately became pregnant. A revolted Gaia refused to have anything to do with a child which Hephaistos had attempted to father on Athene, so she resolved to bring him up herself. He became an important legendary king of Athens.