If Sith Apprentices always kill the master and take their position, why do Sith Lords keep taking apprentices and teaching them their ways?
The Darth Bane trilogy of books explains the concept of the rule of two very well, for starters there are only two Sith because that way the power base is focused. There is not a huge array of Sith fighting each other for power, as is the nature of the dark side and so it is harder for the Jedi to confirm their existence, thus ensuring the continued survival of the true Sith. Because there are only two Sith, a Sith lord MUST take an apprentice, for the power and knowledge of the Sith must not be allowed to die out.
Every Sith master knows his apprentice will try and kill him, as he killed his master before, and most accept this, because it means he has grown weak, while his apprentice is strong, in this way the Sith ALWAYS grow stronger, while the Jedi stagnate, sharing knowledge and power among lesser weak people who should not be allowed to survive.
There are Sith who strive for immortality, thinking they will never find an apprentice strong enough to succeed them; or perhaps being afraid of death, such as Palpatine has tried various times. Palpatine, and those like him have strayed from the Path of two that was instituted by Bane, weakening the Sith and exposing them.
If you like star wars, read the Bane trilogy, they’re fantastic, and Darth Bane is the counter point to Luke Skywalker. Skywalker was the chosen one, and Bane was the Sith’ari, one destined to bring balanced to the dark side. Bane is arguably one of the most important Dark Lords that ever lived, as he completely recreated the Sith.