When writing in first person, you're limited to only what the first person narrator knows. You can't actually include another character's thoughts, as that would be shifting into another perspective. Still, there may be moments where you want to reveal what another character might be thinking and you can accomplish that while still staying in your narrator's perspective.
Let the other character betray his or her thoughts through dialogue or action. In “After the Plague," a short story by T.C. Boyle, disease has wiped out most the population. The plague hits when the narrator has isolated himself in the Sierra foothills. His first human contact after the plague is Sarai, a woman who was hiking and lost her way after her partner disappeared, and who bangs on the narrator's cabin door desperate for help. Sarai doesn't believe the narrator's claim that the population has been wiped out, so after she regains her strength they go into town. Dust has settled on the unused gas pumps at the station, animals have raided the abandoned grocery store and the phone lines are dead. Still, Sarai resists the truth. The narrator decides to go back to the cabin. He is about to try to convince her one last time to join him:
Before I could open my mouth she bent for a stone and heaved it into the windshield, splintering me with flecks and shards of safety glass. “Die!" she shrieked. “You die, you shit!"
That night we slept together for the first time. In the morning, we packed up a few things and drove down the snaking mountain road to the charnel house of the world.
Sarai is angry. Her harsh words make that clear. But she also seems resigned. After all, she returns to the cabin with the narrator instead of striking out on her own in search of other people. The fact that she sleeps with him reveals something more—a need for comfort and companionship.
You can also let the first person narrator consider the other character's thoughts. In “Crazy Life," a short story by Lou Mathews, Dulcie, the narrator, visits her boyfriend in jail. He was involved in a drive-by murder and Dulcie tries to get the true story of what happened from him:
Chuey, I said, were you driving? He just looks at me for awhile and then says, yeah. I ask, How come you were driving?
He had the shotgun, Chuey said, I had to drive.
I can tell when Chuey's lying, which is most of the time; I think he was telling the truth. Chuey, I said. You're crazy. They'll put you both away. You don't owe Sleepy nothing.
There's still some doubt—perhaps Chuey is lying—but the reader relies on Dulcie's knowledge of Chuey to learn more of what may be going on in his mind.
You can also have your first person narrator imagine his way into character's thoughts. In F. Scott Fitzgerald's novel The Great Gatsby, Nick Carraway, the narrator, didn't witness Gatsby and Daisy's first kiss, but he imagines his way into the scene. He also imagines Gatsby's thoughts in the moment:
His heart beat faster and faster as Daisy's white face came up to his own. He knew that when he kissed this girl, and forever wed his unutterable visions to her perishable breath, his mind would never romp again like the mind of God. So he waited, listening for a moment longer to the tuning fork that had been struck upon a star. Then he kissed her.
Did Gatsby actually think that “his mind would never romp again like the mind of God" right before he kissed Daisy? Perhaps. The reader doesn't know how much of this Gatsby has supplied Nick in conversation. He may have told Nick those very words. Or Nick may have invented them based on what Gatsby did share and what he knows about Gatsby's personality. If the reader finds Nick reliable—and most do—they'll likely find this moment quite plausible.
There are point of view strategies that do include multiple first person narrators. Serial first person point of view, for instance, uses a series of first person narratives to tell a story. But when you choose one first person narrator, you still have some room to invite the thoughts of other characters into the story. You just have to do it through the filter of your first person narrator.