What we know is that kings were elected by the people for life. No Roman king ever took power by force, which is quite a remarkable fact. The king was the commander-in-chief of the army and was also the head of the religion: he was in charge of major religious ceremonies and he appointed all the priests. The king was actually considered the bridge to God (hence the latin word pontifex). He was also the head of justice. He was surrounded by advisors and there even was an assembly.
The senators in the Senate were the advisors to the king while the Curiate Assembly was in charge of passing laws that were submitted by the king. Initially, Romulus selected 100 men to become senators, these men were called patres (from the word pater or father) and their descendants became members of what we call the patrician class. All decisions regarding laws were made by the king except for decisions regarding war where he had to get the approval of both the Curiate Assembly and the Senate.
The first king and founder of Rome was Romulus (approximately 753-717 BC, see our section on the founding of Rome) and the king's seat of power was in the Forum. The second King was Numa Pompilius (approximately 716-673 BC) who built large buildings such as the royal palace used by later kings and who also built the Temple of Vesta. He also created Rome's main religious and political institutions and introduced the month of January.
Tullus Hostilius (approximately 673-642 BC) was the third king of Rome and is known for the war with Alba Longa (and the complete destruction of it). We note that Romulus was from Alba Longa which was a city by the sea a few miles away from Rome. The fourth king was Ancus Marcius (approximately 640-616 BC) and is known for the wars with the Sabines and again with Alba Longa. The fifth king was Tarquinius Priscus (approximately 616-579 BC) who is known for building the Circus Maximus.
The sixth king was Servius Tullius (approximately 578-535 BC) who developed Roman coinage. He also developed the Compitalia, which is a festival organized once a year to honor the Lares Compitales which were the household deities. At crossroads (in latin: compitum), sacrifices were offered to these deities. The seventh and last king of the Roman kingdom was Tarquinius Superbus (approximately 535-509 BC).