I hear a lot of people talking about what they do to praise God, so my question is: How do we praise the Father according to His word?
In the Old Testament, on common word that is translated "praise" is tehillah, which literally means "to cause to shine." Thus, praise is giving glory to God. "He put a new song in my mouth, a song of praise to our God; many will see and fear and will trust in the LORD" (Psalms 40:3).
Tehillah comes from a root word, halal, which literally means to shine, to flash forth light. It can be translated as to boast, to exult, or to praise. Psalms 113 explains it well:
"Praise the LORD!
Praise, O servants of the LORD, praise the name of the LORD!
Blessed be the name of the LORD from this time forth and forevermore!
From the rising of the sun to its going down the LORD'S name is to be praised.
The LORD is high above all nations, His glory above the heavens.
Who is like the LORD our God, who dwells on high, who humbles Himself to behold the things that are in the heavens and in the earth?
He raises the poor out of the dust, and lifts the needy out of the ash heap, that He may seat him with princes - with the princes of His people.
He grants the barren woman a home, like a joyful mother of children.
Praise the LORD!" (Psalms 113:1-9).
God's reputation is caused to shine by people exulting the things that God has done.
In the New Testament, ainos, aineo, and ainesis are various forms of a word that literally means to tell a story -- in this case telling a story that exults the things God has done. "Immediately he regained his sight and began following Him, glorifying God; and when all the people saw it, they gave praise to God" (Luke 18:43).
A related word is eulogeo, which literally means to speak good of another. It is what Zacharias did after his voice was returned to him. "And at once his mouth was opened and his tongue loosed, and he began to speak in praise of God" (Luke 1:64).
Another Greek word that is sometimes translated as "praise" is megaluno, which literally means to make great by words. "This became known to all, both Jews and Greeks, who lived in Ephesus; and fear fell upon them all and the name of the Lord Jesus was being magnified" (Acts 19:17).
Finally, the Greek word doxa is sometimes translated as "praise." It refers to what someone thinks of another, or their reputation. Thus, in reference to God, it is giving Him glory and honor. "For from Him and through Him and to Him are all things. To Him be the glory forever. Amen" (Romans 11:36).