Rav Chaim Friedlander asks some incisive questions in regards to the story of Yosef's rise to power, that I believe are very instructive as to what we can expect from a true king of the Jewish people.
He points out that it is remarkable that Yosef was raised to the unbelievable height of power as Egypt's second in command in such a short span of time. He had just come out of jail to attempt an explanation for Paroh's dream, and within moments of giving him a satisfactory answer, he was made the leader of the land. How did Paroh have the confidence in Yosef to give him this position so quickly? Was Yosef the only intelligent person that was around? Giving a good 'pshat' in a dream seems a highly unlikely impetus for such a high-ranking position to be obtained. How do we understand this?
As the story continues, there is continued reason to be amazed. It is clear that the people of Egypt were completely ready (at Pharaoh's command) to do whatever Yosef requested of them. In the end, they willingly chose to be slaves to satisfy Yosef's demands. What was the reason for Yosef's mesmerizing power of the people?
Rav Friedlander notes that if one were to try to figure out how to take control of a group of people so that they would be completely subservient to their ruler, there is only one way to do so where the people serve willingly. This can be accomplished only if the ruler exhibits completely and honestly that he has no concern for himself, and that he is totally dedicated to the needs of his people.
As Yosef entered Paroh's court, the first thing Paroh said was, "I have heard you can hear a dream and interpret it."
Yosef could easily have responded and said, "Yes it is true."
Instead, he took no credit, but rather gave it to Someone else - Hashem. By continuously doing so, he showed that he was not looking for self-aggrandizement, but was truly a servant-leader. Everything Yosef did saw success, because Yosef was never looking for his own benefit, rather for the benefit of others.
In fact, at the end of the story, we find that Paroh specifically tells Yosef to send gifts to his father. Why was it necessary? The meforshim explain that Yosef was so careful never to touch anything that was not his, that if Paroh had not commanded him, he would not have sent anything to his father!
If we want to know what Moshiach will look like, we need look no further than Yosef himself, who was the quintessential Moshiach ben Yosef. His motivation was purely to act as a facilitator for others' benefit, to bring Hashem's goodness to the world and specifically to the Jewish people. Moshiach will have no thought of himself, and will only look to benefit others. He will have a tremendous חן, all will make themselves subservient to him, because they will know that he truly is subservient to them.