Psalm 69:30, "I will praise the name of God with a song, and will magnify him with thanksgiving," is a powerful expression of worship and gratitude. Let's break it down:

"I will praise the name of God with a song":
"Praise": This goes beyond simply acknowledging God's existence. It means actively and enthusiastically expressing admiration, respect, and gratitude for who He is and what He has done. It's a deliberate act of honoring God.
"The name of God": In Hebrew thought, a person's name represented their character, reputation, and essence. Praising God's name means praising His entire being – His attributes, His power, His love, His justice, His mercy, etc.
"With a song": This indicates that the praise will be expressed through music and singing. Song is a powerful medium for conveying emotions and expressing devotion. It suggests a heartfelt and joyful offering to God.

"And will magnify him with thanksgiving":
"Magnify": This means to make something appear greater, larger, or more important. In the context of God, it doesn't mean literally making Him bigger (since He is already infinite), but rather making His greatness known and appreciated by oneself and others. It's about highlighting His significance and impact.
"With thanksgiving": This emphasizes the motive behind magnifying God. It's not empty flattery, but genuine gratitude for His blessings, His faithfulness, and His goodness. Thanksgiving is the foundation upon which true praise is built.

In essence, the verse is a commitment to:

Express heartfelt worship through music.
Acknowledge and celebrate God's character and attributes.
Make God's greatness known and appreciated.
Offer sincere gratitude for all that God has done.

The overall meaning is that the speaker is determined to actively and joyfully express their devotion to God through praise and thanksgiving. It's a promise to focus on God's goodness and to share that appreciation with others.