How did the plebeians gain political rights

Plebeians were the general body of small landowners of Roman citizens in Ancient Rome. They were distinct from the higher class of patricians. In Rome, plebeians could become quite wealthy and influential. 
During the reign of Ancus Marcius, the plebeians came to Rome as second-class citizens from other parts of Italy and surrounding territories. At the foundation of the Roman Republic, plebeians were excluded from religious office or acting as magistrates, and the law of the Twelve Tables prohibited intermarriage with patricians. Even so, plebeians were enrolled in the gentes and tribes, served in the army, and could become military tribunes. 
The "Conflict of the Orders" over the political status of the plebeians continued for the first two centuries of the Republic, ending with the formal declaration of equality of plebeians and patricians in 287 BC. The plebeians achieved this by developing their own organisations (the "concilium plebis") and leaders (the tribunes and "plebeian aediles"). 
The ultimate weapon in the clash of the social orders was the threat of "secessio", by which the plebeians would literally leave Rome, thereby boycotting the city, the shops, the houses and trade in general. That threat to patrician wealth was too great and the Republic eventually agreed to their equality.