"Then God remembered Noah, and every living thing, and all the animals that were with him in the ark. And God made a wind to pass over the earth, and the waters subsided. The fountains of the deep and the windows of heaven were also stopped, and the rain from heaven was restrained. And the waters receded continually from the earth. At the end of the hundred and fifty days the waters decreased. Then the ark rested in the seventh month, the seventeenth day of the month, on the mountains of Ararat. And the waters decreased continually until the tenth month, on the first day of the month, the tops of mountains were seen" (Gen. 8:1-6).
To say that God "remembered Noah" is not to imply that He had forgotten him; rather, it is to emphasize a blessing God is going to bestow. Without God's intervention, it would have taken a very long time for the floodwaters to subside. God restrained the rain and used wind to cause the waters to recede more rapidly (cf. Psa. 104:5-9). After 5 months, the waters had diminished enough for the ark to come to rest on the mountains of Ararat. But, Noah and his family would still have many more months living inside the ark while the water levels continued to decrease. Although they were resting on top of a mountain, the situation was such that they could not see any other mountains for another two and a half months. No doubt they were all getting anxious to exit the ark and set foot on dry land, but the time was not yet ready.
"So it came to pass, at the end of the forty days that Noah opened the window of the ark which he had made. Then he sent out a raven, which kept going to and fro until the waters had dried up from the earth. He also sent out from himself a dove, to see if the waters had receded from the face of the ground. But the dove found no resting place for the sole of her foot, and she returned into the ark to him, for the waters were on the face of the whole earth. So he put out his hand and took her, and drew her into the ark to himself" (Gen. 8:7-9). About six weeks after the ark came to rest on the mountain, a raven is sent out. Even though the land was not yet dry, it would land anywhere possible. A dove is also sent out of the ark. Unlike the raven, the dove would only land on a dry surface. Noah is testing to see if the time is right for his family to leave the ark. As long as the dove continued returning to Noah, he knew they needed to remain in the ark.
"And he waited yet another seven days, and again he sent the dove out from the ark. Then the dove came to him in the evening, and behold, a freshly plucked olive leaf was in her mouth; and Noah knew that the waters had receded from the earth. So he waited yet another seven days and sent out the dove, which did not return again to him anymore. And it came to pass in the six hundredth and first year, in the first month, the first day of the month, that the waters were dried up from the earth; and Noah removed the covering of the ark and looked, and indeed the surface of the ground was dry. And in the second month, on the twenty-seventh day of the month, the earth was dried" (Gen. 8:10-14).
The waiting continued. Finally, a dove returned to the ark with an olive leaf! Interestingly, I have read that olive trees can produce leaves even when submerged in water! After over ten months in the ark, Noah removed the roof of the ark and was able to see that the "surface of the ground was dry." Apparently it wasn't dry enough to leave the ark just yet, however, for Noah and his family remained on board nearly two more months.
"Then God spoke to Noah, saying, 'Go out of the ark, you and your wife, and your sons and your sons' wives with you. Bring out with you every living thing of all flesh that is with you: birds and cattle and every creeping thing that creeps on the earth, so that they may abound on the earth, and be fruitful and multiply on the earth' (Gen. 8:15-17). Noah waits for God's instructions always--even regarding when they should exit the ark. In total, they remained on the vessel just over one year. They would emerge to a much different planet. The environment was changed, their old neighbors were gone, and life would have been full of peace and righteousness--at least for a while.