Act I
Visit to a Small Planet opens with a view of television news commentator Roger Spelding's comfortably middle-class home near Manassas, Virginia. General Tom Powers, a friend of Roger's, is explaining to him that an Unidentified Flying Object (UFO) has, for the last twelve hours, been spotted hovering over the Spelding's home. When Roger dismisses the idea, Powers convinces him to look outside—which he does, seeing the craft. Roger, who was planning to announce to a television audience that UFOs do not exist, panics and asks Powers for permission to break the story. The general refuses, stating that this information is "classified."

Ellen, Roger's nineteen year-old daughter, then appears on the terrace with her boyfriend Conrad Mayberry, whom Roger dismisses as "the boy farmer." She and Conrad discuss their plans for the future; these plans are interrupted, however, when the UFO lands outside the house. The hatch opens and Kreton, the visitor from outer space, enters the room. He looks very human, sporting side-whiskers and the garb of an 1860s gentleman. Kreton asks the Speldings to take him to General Robert E. Lee. After some confusion, Kreton explains that he has been studying the inhabitants of Earth as a ' 'hobby''; he hoped to see the Civil War Battle of Bull Run. He soon realizes, however, that he must have set the wrong coordinates for his time-traveling spacecraft. Invited by Roger (who hopes to interview him on his television show) to come inside, Kreton accepts, thrilled with the prospect of seeing "a real house.''

General Powers returns with an aide and in Roger's study begins questioning Kreton. We learn that Kreton is not only from another planet but from another dimension, one where its inhabitants do not die and have the power to read minds—a power that Kreton demonstrates on the general. After being ordered by Powers to search Kreton's ship, the aide returns, explaining that the door has been shut and that there has been "some kind of invisible wall" constructed around it. When asked by Powers how he managed to create this force field, Kreton dryly responds, "I don't think I could ever explain it to you.'' Powers then announces that no one present is allowed to leave the house. The general presses his investigation of Kreton, speculating that he "has been sent here by another civilization for the express purpose of reconnoitering prior to invasion." Kreton denies that he has been "sent here" by anybody—but then explains that he intends to "take charge" of the entire world. When Powers attempts to arrest him, Kreton surrounds himself with another invisible force-field. The curtain closes as the audience hears all of the characters' thoughts and Kreton saying,' 'Tomorrow will be a wonderful day for all of us. Sleep tight!"

Act II, Scene 1
The next morning Kreton is found in the living room examining a globe and talking to Rosemary, the Speldings' cat, whose thoughts he can also read and understand. Roger has left for Washington with General Powers, Reba (Roger's wife) has received permission to go shopping and Conrad is still asleep upstairs. Ellen brings Kreton his breakfast, which he refuses because he never eats. He also tells Ellen that the inhabitants of his world have given up reproducing, since they never die. Finally, he explains that after they ' 'wiped out'' diseases such as scarlet fever, mumps, and the common cold, the inhabitants of his planet rid themselves of "the ultimate disease:" passion. As a result, Kreton explains "We feel nothing. We do nothing. We are perfect." Ellen learns that this lack of passion or any strong emotion is what initially led Kreton to travel to earth and escape his dull commander, Delton 4.

Ellen and Kreton grow friendlier, and Ellen convinces the alien to give her a lesson in the mind-tricks that he has been using throughout the play. Eventually, she is able to levitate a vase over the fireplace mantle for a few seconds, much to the surprise of Conrad, who watches in awe. Kreton next begins thinking about how he will take over the planet, deciding against "drying up one of the smaller oceans" or "monkeying around with the moon" in favor of a more subtle trick. At that moment, the audience sees the aide (who is stationed on the porch) watch in disbelief as his rifle leaps from his hands into the air. Kreton explains that he has just made all of the rifles in the world levitate for fifteen seconds.

General Powers returns and tells Kreton that he has been recently "classified as a weapon" and that the United States government expects him to furnish "a comprehensive list" of his "various mental powers." Roger enters with the alarming news that "at eleven twenty-six this morning every rifle in the Free World was raised fifteen feet in the air and the lowered again." Never considering the possibility that this was one of Kreton's tricks, Roger concludes, "It's the Russians, obviously." Kreton then explains the real purpose of his latest trick to the cat:' 'Well, I do believe I have started a war.,.. After all, that's what I came down here to see!"

Act II, Scene 2
Roger delivers a newscast from his study, interviewing General Powers, who tells the viewing audience that "it doesn't look good." Upstairs, Kreton enjoys his first bath while Roger informs Conrad—an avowed pacifist who hates all forms of war—that he should enlist in the Army. Conrad refuses and asks Ellen to marry him, but she refuses on the grounds that Conrad lacks "drive." Kreton comes downstairs, wearing full Confederate Army garb, and begins testing Conrad's pacifism by singing a series of patriotic songs. Conrad remains unmoved. As a last resort to incite Conrad's' 'primitive" urge to fight, Kreton broadcasts the mind of Powers's aide as he looks at Ellen; when Conrad hears these thoughts that refer to Ellen as ' 'the babe with the crazy build," he attacks the aide and Kreton watches the fistfight, delighted. Ellen is also impressed and agrees to marry Conrad because of this display of love. As the young lovers exit, Powers enters and is told by Kreton that he has (again using the powers of his mind) "arranged a sneak attack" of United States bombers on Russia. In exactly forty-seven minutes, the world will reach "zero hour."

Act III
It is a half-hour later, and Kreton has transformed the Speldings' living room into a command center, using toy planes and soldiers to simulate the upcoming destruction. Powers reports that the Russian military is "completely mobilized" and enjoys a last drink with Kreton. Conrad and Ellen beg Kreton to stop the upcoming war, but Kreton explains that "war is not only fun," but "creative," since so many of humanity's great inventions were made during wartime. Ellen then tricks Kreton into telling her how he would contact his leader, Delton 4, if he so needed; Kreton's answer, "concentration," inspires her to attempt a "mind-trick" similar to the one she performed in Act II. As the cast rushes about the stage, Ellen sits on the sofa repeating, "Delton 4 ... Delton 4 ... Delton 4," until Kreton's leader arrives in answer to this call. Dressed in a suave morning suit, Delton 4 thanks Ellen for the warning and explains that Kreton ' 'is a rarity" among those of his planet, for "he is morally retarded and, tike a child, regards this world as his plaything." He also tells the cast that Krelon had "escaped from his nursery" and that he will take him back home, Kreton says goodbye, remarking that he actually envies earthlings for "being so violent... so loving ... so beautifully imperfect" and "so much happier'' than they realize. Once the aliens leave, time shifts back to the exact moment before Kreton arrived, leaving the characters with no memory whatsoever of the events that have just taken place.