For those Christians who take this event literally, the majority would understand this (based on our modern understanding of the relative motion and position of the earth to the sun) as the earth being made still--the naturalistic effects that such would cause are waved away by simply acknowledging God's supreme power and authority over His creation. If God wanted to make the earth stop spinning without the problems that would cause, He can certainly do that.
In other words, God can do what God wants to do, He's God.
Other Christians may take a less literal approach to the story, or have other explanations.
Those Christians who insist on a geocentric (or even flat earth) perspective would argue that the sun literally stopped moving because the sun, not the earth, is what moves.
As for me, personally, I don't worry too much about how literal or non-literal the event is; though I would be fine with a simple acknowledgment that God did something to help the Israelites. Perhaps it only appeared that the sun stopped moving, or perhaps this meant something we don't fully understand now to the ancients who wrote about it. Or perhaps God literally compelled the earth to stop moving about its axis and because He's God, He can do that. Whatever the case may be, it's not one of those things that I think is particularly important to the overarching divinely inspired narrative of Holy Scripture.
The importance of Israel's entrance into the land of promise is ultimately about Jesus. Because the Bible is always about Jesus.
-CryptoLutheran