And prompted by the [Holy] Spirit, he came into the temple [enclosure]; and when the parents brought in the little child Jesus to do for Him what was customary according to the Law, [Simeon] took Him up in his arms and praised and thanked God and said...(Luke 2:27, 28 AMP)
The Priest in the Temple at Jerusalem was praying for the Messiah's entrance for decades. He felt the Lord tell him he would not pass away until he had seen Him. He happened to come into the enclosure after all these years and who should be there but the little seven day old Messiah and His mom and dad. Simeon knew immediately. There's something in our spirit that is warmed when the Messiah is near. There were some rituals to do then Simeon took Him in his arms and held and cuddled Him. He reveled in who he was holding...a tiny babe, the powerful Messiah. There are times when a song or a piece of Scripture are all that'll do to give the Lord in return for what He gave us. So Simeon sang or prayed his thanks to His heavenly Father for the privilege.
Maybe it was something like this:
"Name above all names
Worthy of our praise
My heart will sing
How great is our God
How great is our God, sing with me
How great is our God, and all will see
How great, how great is our God"...Chris Tomlin
Then He told God "I'm ready. Take me Home when You're ready. I'm at peace."