She was married to John Comnenos, younger brother of Isaac I Comnenos, who rebelled in 1057 against the current emperor and took the throne. This placed John himself (and therefore Anna) closer to the seat of power, and may have served to increase her ambitions for her children.
She and John had eight children. When Isaac decided to abdicate the throne to become a monk, John declined the throne, despite Anna's vehement urging about the benefits the position would create for their children. The throne went to Constantine X Doukas, whose family Anna then considered a rival that must be opposed.
Constantine died in May of 1067, the throne passing to Romanos IV Diogenes. John died 12 July of that same year, and Anna became responsible for raising the children and finding opportunities for them. She allied herself with Constantine's widow, with whose help she arranged politically advantageous marriages for her children. She also allied herself with Romanos, supporting him against the Doukas clan. Anna's youngest daughter, Theodora, was married to Romanos' son. Her eldest son, Manuel, became one of Romanos' best generals. (Manuel died from infection in 1071, and she tried to put Alexios forward as a suitable replacement in his position, but Alexios was considered too young at the time.)
Romanos IV was captured by the Seljuk Turks in August 1071, and the Doukas clan returned to power with Michael VII Doukas taking the throne. When Romanos was freed from the Seljuks, the Doukas clan led troops against him, capturing him to prevent a return to power and blinding him. Anna was accused of supporting Romanos, even being brought to trial.
She was prepared. She boldly pulled a crucifix from under her cloak and said "Here is my judge and yours. Think of him before deciding and take heed that your decision is worthy of the supreme judge, who knows the secrets of men's hearts." She and her sons were exiled to the island of Prinkipos. After Romanos died and there was no chance of a rebellion coalescing around him, they were allowed to return from exile. Michael VII even seemed to try to win her over by allowing Anna's son Isaac to marry his wife's cousin. Also, Alexios was married in 1078 to the 12-year-old Irene Doukaina, niece of Constantine X Doukas.
So it looked like her desire for her children to be secure and successful was coming true. There was more to come, however, because in 1081 the Comnenos clan and Anna would pull off a coup d'état, the details of which you will read tomorrow.