For a Padawan to become a Knight, they had to pass the Trials of Knighthood. These tests were administered by the High Council, to Padawans they believed to be ready. While age did not directly play a part in the Council’s decision to have someone take the tests, most Padawans were knighted in their twenties. The Master’s approval was not required, though I believe that they could recommend that their Padawan be tested.
During the Trials of Knighthood, a Padawan had to pass five trials: the Trials of Skill, Courage, Spirit, Flesh, and Insight. If deemed appropriate, the Council may have also substituted tests or waived them if the Padawan had shown the same qualities through their actions. For instance, both Anakin and Obi-Wan became Knights without participating in formal trials.
For the Trial of Skill, one must face a three-part assessment consisting of physical, mental, and combat challenges. The physical challenges were usually tests of strength, endurance, climbing, jumping and the like. The mental challenges were tests of levitation, another endurance test, duress and reflection. For the combat challenges, Padawans completed tests of conflict, duelling, and of the calm mind, and were required to face some sort of adversary. The individual or individuals they face would vary a lot, from holograms to droids to other students, or even the Temple Battlemaster or Grand Master. Some students may fight many opponents using many different weapons or altering the appearance of the chamber or their perception. While the tests largely consisted of physical feats, the Battlemaster looked more for the ability of a Padawan to use discipline and focus to avoid distraction. Anakin completed this trial when he defeated Asajj Ventress in combat.
Less is known about the Trial of Courage. In order for the test to work, the student must not know beforehand what they will face. Before the Golden Age of the Republic, courage on the battlefield or facing a Sith was considered a good way to pass the trial, but later tests were largely simulated. The Council could also send a student on a real mission; these missions had the potential to be deadly, which is why only students who are ready may participate in the Trials. When Obi-Wan defeated Darth Maul on Naboo, the Council considered that his Trial of Courage.
The Trial of the Spirit was a test of self-discovery. A Padawan entered a deep meditative trance and confronted their deepest fears and the darkness within themselves. Such deep meditation could be very dangerous, so a Master was always present to help guide the student back to the present. Unlike other tests, the High Council did not dictate what would happen and the student would have to decide what to do on their journey. This test had the potential to be highly traumatising, and some students would wake from a failed test inconsolable.
The Trial of the Flesh was considered the hardest test of the five, and it involved the Padawan experiencing great physical pain, loss, or hardship. In the earlier days of the Republic, the students were subjected to bursts of electricity applied directly to the skin, but this practice was abandoned. During the New Sith Wars, battle scars and lost limbs were often accepted as a way to pass the test. It was not uncommon for a Padawan to pass the Trials of the Flesh, Skill and Courage at the same time by defeating a Sith on the battlefield. Later, the separation of the Master-Padawan pair as the Padawan became a Knight was considered a hardship enough to pass the test, but during the Clone Wars it was once again common to pass through physical injury and loss.
The Trial of Insight was a test that required the Padawan to use the Force to see through deception. To pass, they were forbidden to study any possible challenges in the Archives, as they had to complete it themselves. The Trial sometimes took the form of riddles and puzzles, such as being required to solve the High Riddles of Dwartii. Other known scenarios are having to find one grain of sand among a field of rocks, or being faced with an army of holograms and forced to see through the illusion.
If a Padawan passed all these tests in one way or another, their Master would then prepare them for the Knighting Ceremony. If they failed, they had the opportunity to take them again until they passed. Before the ceremony, the student would meditate in the preparation room in the Tranquility Spire for a whole day. The next day, they would go up to the next level of the Tower, called the Hall of Knighthood. There, they would kneel in front of the Grand Master, the members of the High Council (if the High Council was unavailable, members of the other two Councils would step in), and other Jedi who were influential in the Padawan’s journey. The present Masters would ignite their lightsabers in a circle around the apprentice, and the Grand Master would lower their lightsaber to just above each of the student’s shoulders before severing their braid. The new Knight would then take their braid and leave the Hall in silence.
During Kanan’s knighting during a vision in the Lothal Jedi Temple, the words said were, “By the right of the Council, by the will of the Force, Kanan Jarrus, you may rise.” This may have also been said during more orthodox ceremonies, or another similar phrase.
Hopefully that’s helpful, and good luck!
~ Jacen