“Therefore by Him (Jesus) let us continually offer the sacrifice of praise to God, that is, the fruit of our lips, giving thanks to His name.”  
Hebrews 13:15 

To me this verse can be looked at in three parts.  So let us see what Scripture tells us of the ‘sacrifice of praise’ ‘the fruit of our lips (how we praise Him) and ‘giving thanks to His name.’  The Thompson Chain Reference is our study guide as we look into each part.  This by far is NOT an exhaustive study, but hopefully it is an encouragement to do a personal further study.

Sacrifice of praise--
“Let them sacrifice the sacrifices of thanksgiving’
And declare His works with rejoicing.”  Psalm  107:22

“I will offer to You the sacrifice of thanksgiving,
And will call upon the name of the LORD.”  Psalm 116:17

“And they shall come from the cities of Judah and from the places around Jerusalem, from the land of Benjamin and from the lowland, from the  mountains and from the South, bringing burnt offerings and sacrifices,  grain offerings and incense, bringing sacrifices of praise to the house of the LORD.”  Jeremiah 17:26

Jonah from the belly of the fish, verse 9,
“But I will sacrifice to You
With the voice of thanksgiving;
I will pay what I have vowed.
Salvation is of the LORD.”  Jonah 2:9

The fruit of the lips--
“Sing praises to the LORD, who dwells in Zion!
Declare His deeds among the people.”  Psalm 9:11

“Let the people praise You, O God;
Let all the people praise You.”  Psalm 67:3

“Let them give glory to the LORD,
And declare His praise in the coastlands.”  Isaiah 42:12

1 Peter 2:9 states so clearly why we continually praise our marvelous loving gracious Lord,
“But you are a chosen generation, a royal priesthood, a holy nation, His own special people, that you may proclaim the promises of Him who called you out of darkness into His marvelous light.”

Giving thanks (testimony) to His name--
Unceasingly:
“I have set a watchman on your walls, O Jerusalem,
Who shall never hold their peace day or night.
You who make mention of the LORD, do not keep silent.”  Isaiah 62;6

Mark 5:18-19 tells of the demon possessed man whom Jesus healed and who wanted to be with Jesus,
“When He (Jesus) got into the boat, he who was demon-possessed begged Him that he might be with Him.
However, Jesus did not permit him, but said to him, ‘Go home to your friends, and tell them what great things the Lord has done for you, and how He has had compassion on you.’”

Acts 1:8 Jesus is speaking,
“But you shall receive power when the Holy Spirit has come upon you; and you shall be witnesses to Me in Jerusalem, and in Judea and Samaria, and to the end of the earth.”

Paul to Timothy in 2 Timothy 1:8
“Therefore do not be ashamed of the gospel of the testimony of the Lord, nor of me, His prisoner, but share with me in the suffering for the gospel according to the power of God.”

“But sanctify the Lord God in your hearts, and always be ready to give a defense to everyone who asks you a reason for the hope that is in you, with meekness  and fear.”  1 Peter 3:15

So let us do just that:
“Let us continually offer the sacrifice of praise to God, that is, the fruit of our lips, giving thanks to His name.”  
WE love You Lord because You first loved us!  And You went to the cross to pay for our sin debt!  You imputed Your righteousness to us in exchange for our sin debt!  Oh most gracious, loving, merciful, gentle, good God; how grateful we are! Thank you.  Amen