Who should praise the Lord?

Everything that hath breath.

Read Psalms.

The people of God:

Psalm 79:13

But we your people, the sheep of your pasture, will give thanks to you forever; from generation to generation we will recount your praise.

The righteous

Psalm 140:13

Surely the righteous shall give thanks to your name; the upright shall dwell in your presence.

The saints

Psalm 145:10

All your works shall give thanks to you, O LORD, and all your saints shall bless you!

The redeemed:

Psalm 107:1-2

Oh give thanks to the LORD, for he is good, for his steadfast love endures forever!
  Let the redeemed of the LORD say so, whom he has redeemed from trouble

Those who fear the Lord:

Psalm 22:23

 You who fear the LORD, praise him! All you offspring of Jacob, glorify him, and stand in awe of him, all you offspring of Israel!

Those who know and believe the truth:

1 Timothy 4:3

Who forbid marriage and require abstinence from foods that God created to be received with thanksgiving by those who believe and know the truth.

The servants of God:

Psalm 113:1

Praise the LORD! Praise, O servants of the LORD, praise the name of the LORD!

Psalm 134:1

Come, bless the LORD, all you servants of the LORD, who stand by night in the house of the LORD!

Psalm 135:1

Praise the LORD!  Praise the name of the LORD, give praise, O servants of the LORD,

All His angels:

Psalm 148:2
Praise him, all his angels; praise him, all his hosts!

All nature:

Read - Psalm 148:3-10