Short answer: Rain and Underground Water
Bible Text: Genesis 7:11-12
“In the six hundredth year of Noah’s life, in the second month, on the seventeenth day of the month, on the same day all the fountains of the great deep burst open, and the floodgates of the sky were opened. The rain fell upon the earth for forty days and forty nights”
Some folks object that 40 days and nights of rain just isn’t enough to cover the whole earth. Especially not the mountains we see today. So first we must ask where did all of that water come from?
Creationists believe that when the fountains of the great deep burst open that this likely refers to underwater reservoirs bursting forth in geysers. Keep in mind that Genesis 2:6 says “a mist used to rise from the earth and water the whole surface of the ground,” which also seems to refer to underground water reservoirs. This provided the extra water for the Flood.
As for how this was able to cover the “high hills,” we note that Psalm 104:5-9 says that at the end of the Flood the “mountains rose, the valleys sank down,” implying that the topography of the pre-Food and post-Flood Earth were dramatically different. In other words, the pre-Flood world’s topography was less exaggerated than it is today. When you consider that if the Earth’s topography were leveled [above and below the oceans] the water would cover its surface by 1.7 miles, it’s not hard to see how the pre-Flood world was covered.