I believe Asaf is speaking in Psalm 82:1 (ESV):
A Psalm of Asaph.
God has taken his place in the divine council; in the midst of the gods he holds judgment:
Then God is speaking in Psalm 82:2-4:
How long will you judge unjustly and show partiality to the wicked? Selah Give justice to the weak and the fatherless; maintain the right of the afflicted and the destitute. Rescue the weak and the needy; deliver them from the hand of the wicked.
I believe Asaf or God could be speaking in Psalm 82:5:
They have neither knowledge nor understanding, they walk about in darkness; all the foundations of the earth are shaken.
It's hard to say. But, who is speaking in Ps. 82:6 (I said, "You are gods.")?
I said, You are gods, sons of the Most High, all of you; nevertheless, like men you shall die, and fall like any prince.
(Quotation punctuation, which was added by the translator and did not exist in Biblical Hebrew, has been removed.)
Is there some way to determine who is calling people "gods"?
Clearly it's Asaf speaking in the final verse:
Arise, O God, judge the earth; for you shall inherit all the nations!