"Then Moses and the children of Israel sang this song to the LORD, and spoke, saying: 'I will sing to the LORD, for He has triumphed gloriously! The horse and its rider He has thrown into the sea! The LORD is my strength and song, and He has become my salvation; He is my God, and I will praise Him; my father's God, and I will exalt Him. The LORD is a man of war; the LORD is His name. Pharaoh's chariots and his army He has cast into the sea; his chosen captains also are drowned in the Red Sea. The depths have covered them; they sank to the bottom like a stone" (Exo. 15:1-5).
Further along in the poetic lyrics, a significant rhetorical question is asked - "Who is like You, O LORD, among the gods? Who is like You, glorious in holiness, fearful in praises, doing wonders?" (15:11). All the Israelites should have known the answer to this question by this point or else they never would. God's miraculous actions proved conclusively that there was no god like Jehovah! Indeed He had shown His dominance in manifold ways over the impotent Egyptian gods (cf. Num. 33:4).
The song also makes reference to the impact the destruction at the Red Sea would have upon other nations - "The people will hear and be afraid; sorrow will take hold of the inhabitants of Philistia. Then the chiefs of Edom will be dismayed; the mighty men of Moab, trembling will take hold of them; all the inhabitants of Canaan will melt away. Fear and dread will fall on them; by the greatness of Your arm they will be as still as a stone, till Your people pass over, O LORD, till the people pass over whom You have purchased" (15:14-16). This proved to be precisely the case, as is seen later in the Israelite's history (e.g., Josh. 2:9-11). Israel's reputation spread far and wide. Sadly, the boldness Israel expressed here does not last long enough (e.g., Num. 13 & 14). It was easy for them to rejoice in a victory they had done little to accomplish, and this may partially explain their vacillating nature. How deeply did these words actually sink in? Did they really mean what they were affirming in song? Do we?
The lyrics of Moses' song (cf. Rev. 15:2-4) close with these sentiments directed toward God regarding the children of Israel - "You will bring them in and plant them in the mountain of Your inheritance. In the place, O LORD, which You have made for Your own dwelling, the sanctuary, O LORD, which Your hands have established. The LORD shall reign forever and ever" (Exo. 15:17,18). God was reigning, and He would bring them into their inheritance, Canaan.
It was a glorious day for Israel, and the men and the women (including Moses' older sister, Miriam) celebrated God's great deliverance - "Sing to the LORD for He has triumphed gloriously! The horse and its rider He has thrown into the sea!" (15:21). Since the text says that Miriam "answered", it seems to be the case that Moses led the song for the men and Miriam led the women as they echoed the same lyrics (cf. 15:1).