After many days the word of the LORD came to Elijah, in the third year, saying, “Go, show yourself to Ahab, and I will send rain upon the earth.” (1 Kings 18:1) [ESV]
While a literal reading suggests all that is necessary for rain, is for Elijah to show himself to Ahab, the events which follow show that is an incomplete understanding of the word of the LORD. Obviously when Elijah first shows himself to Ahab, there is no rain, nor is rain part of the discussion:
17 When Ahab saw Elijah, Ahab said to him, “Is it you, you troubler of Israel?” 18 And he answered, “I have not troubled Israel, but you have, and your father's house, because you have abandoned the commandments of the LORD and followed the Baals. 19 Now therefore send and gather all Israel to me at Mount Carmel, and the 450 prophets of Baal and the 400 prophets of Asherah, who eat at Jezebel's table.” (1 Kings 18)
The "word of the LORD" which Elijah received must have included the instructions to arrange the confrontation on Mount Carmel with the 450 prophets of Baal and 400 prophets of Asherah. Also, it is clear Ahab attributes the drought to Elijah, not to the LORD. For Ahab, Elijah is the cause of the drought. For Elijah, Ahab's leadership is the reason the LORD caused the drought. In other words, if rain came just as a result of Elijah appearing to Ahab, Ahab would continue to see this national disaster as something from Elijah, not as something from the LORD in response to Ahab's leadership of the nation.
The underlying cause of the drought was Ahab's actions: abandoning the commandments of the LORD. The proper way to bring the drought to an end should have come from Ahab. He should have turned away from the Baals and to the LORD; he should have rid the land of the prophets of the Baals and of Asherah. That is to say, in the same way Ahab's wrong actions caused the LORD to respond by withholding rain, Ahab's right actions would have caused the LORD to give rain.
The point is the LORD does act in response to a leader's actions. When Ahab fails to respond, despite the events on Mount Carmel, Elijah has the opportunity to take matters into his hands. Notice the LORD simply tells Elijah, "I will send rain upon the earth." He doesn't say when He will do that. Obviously it did not happen immediately after the fire at Mount Carmel.
After ridding the land of the false prophets, Elijah could have simply "called it day" and wait for the rain which was sure to come. However, Elijah knows the LORD responds when a leader demonstrates they are committed to following the commandments of the LORD. What Elijah does next can be seen as something to cause the LORD to send rain right away, in response to Elijah.
The phrase, "I will send rain upon the earth..." recalls the first time the LORD sent rain:
For in seven days I will cause it to rain on the earth for forty days and forty nights, and I will wipe from the face of the ground every living thing that I have made.” (Genesis 7:4)
In addition, the waiting period Noah is repeated two more times:
He waited seven more days and then sent out the dove again from the ark. (Genesis 8:10)
He waited another seven days and sent the dove out again, but it did not return to him this time. (Genesis 8:12)
Elijah knows seven days is the normal time to wait for rain, and it is the normal time man can wait. So rather then wait seven days for the rain which is sure to come, Elijah sends his servant seven times to look for rain. Elijah's actions demonstrate he knows the normal wait time for rain and for relief is seven days. By sending his servant to look for rain seven times on the same day, Elijah causes the LORD to respond and send the rain that day.