Let Us make man in our image
There are several verses in the Old Testament where God speaks as a plurality. Many trinitarians quote these verses to help support the Trinity doctrine because they strongly suggest that there is more than one person in the godhead.
Those opposed to the doctrine of the Trinity say that God is speaking of Himself in any "royal" sense, in a "plural of majesty." They can say this, but biblically there is never any account of a king or a ruler speaking of himself in a plural sense or in the third person. So, there is no biblical support for God using it of Himself in this way.
In regards to Gen. 1:26, those who deny the Trinity say that God when God says, "Let Us make..." He is speaking with the angels in mind. The problem with this is that angels do not create. There is absolutely no biblical evidence that angels created anything at all. We see in Isaiah 44:24, "Thus says the Lord, your Redeemer, and the one who formed you from the womb, “I, the Lord, am the maker of all things, Stretching out the heavens by Myself, And spreading out the earth all alone." God made all things alone. Therefore, the "us" in "Let Us make man in our image" cannot be the angels. Furthermore, people are not created in the image of angels, but of God.
The three verses in Genesis do not prove that the Trinity is true. However, they cannot be dismissed by the assumption that God is speaking of himself in a type of third person way.
Furthermore, notice in the force verse above, Isaiah 6:8, that's God is speaking in the singular and then switches to the plural. He says, "Whom shall I send, and who will go for Us?" This is on the unusual construction. The singular speaker refers to himself in the plural.