Psalm 66:17, "I cried to him with my mouth. He was extolled with my tongue," speaks about a two-fold aspect of prayer and praise:

"I cried to him with my mouth": This refers to the act of praying audibly. It suggests a heartfelt plea or supplication made verbally to God. The word "cried" implies urgency and sincerity. The psalmist is expressing their needs and desperation in a direct way, asking for God's help.

"He was extolled with my tongue": This signifies praising God verbally. "Extolled" means to praise highly or glorify. It indicates that along with asking for help, the psalmist also sang God's praises. They expressed their gratitude, acknowledged God's power and goodness, and celebrated his attributes aloud.

In essence, the verse describes a comprehensive approach to communicating with God:

It's about both petition and praise, asking for help while also acknowledging God's worthiness of adoration.
It highlights the power of vocal prayer and worship. It's not just about thinking about God, but expressing our feelings and thoughts audibly.
It suggests that even in times of need, praise should be part of our communication with God. It keeps our focus on God's character and ability to act.

Here's a simpler way to put it: "I prayed loudly to God when I needed help, and I also praised him loudly for who he is."