How does Sancho Panza show loyalty to his master, Don Quixote, and his friend Alonso Quijana?

Don Quixote and Alonso Quijana are the same person. Don Quixote started life as Alonso Quijana, and Sancho and his wife were Quijana's loyal servants. Quijana is a typical gentleman of his time and place. However, because he gets so involved with reading romance novels, he falls into insanity. He decides, at about age 50, that he too wants to be a noble knight going on adventures. As we know, he lives out his fantasy, renaming himself Don Quixote. Quixote heads off on his quests, taking Sancho Panza with him as his squire. In short, Quixote is the insane version of Alonso Quijana.
Sancho changes from servant to squire, but in both roles, he is pragmatic and loyal to his master. Nevertheless, he is also loyal to himself. He comes with Don Quixote, for example, because he is offered the governorship of an island, which he eventually gets. He is not one to put himself unnecessarily in harm's way for his master, and he is out to make money for himself. All the same, he shows his loyalty by not abandoning Quixote. Sancho says of his master:

He is so simple, that I cannot help loving him with all my heart and soul, and cannot leave him in spite of all his follies.

As the above quote indicates, the insane Don Quixote requires more protection than the sane Alonso Quijana ever did, so Pancho's practical sense becomes more important than it was than when he was the sane man's servant. Sancho cannot stave off most of Quixote's missteps, but he does try. For example, he shows his loyalty when he tries to warn Quixote that what he believes is an attacking army is merely a herd of sheep. When Quixote thinks a basin is King Mambrino's enchanted helmet, Sancho tries to get him to see reality. The squire also is (usually) there to pick up the pieces when Quixote ends up beaten and bruised. He may sometimes jeer at his master, but he sticks with him.
When Quixote is on his deathbed, Sancho, in another show of loyalty, urges him to get well because of the knightly deeds he has yet to accomplish.
Sancho is a complex character who can be both loyal to Quixote and self-interested, as most people are. Nevertheless, he remains the figure of the devoted sidekick, the person with less power but more common sense.