Not only does God refer to Himself with the plural pronoun in Genesis 3, but He also does so in Genesis 1:
Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth. Genesis 1:26 ESV
The first two verses of Genesis 1 are instructive here:
In the beginning, God created the heavens and the earth. 2 The earth was without form and void, and darkness was over the face of the deep. And the Spirit of God was hovering over the face of the waters. Genesis 1:1-2 ESV
The Hebrew word that is translated "God" is actually a noun in plural form--Elohim. The Bible emphatically asserts that God is, in fact, one. There is one God and no other.
Hear, O Israel: The Lord our God, the Lord is one. Deuteronomy 6:4 ESV
I am the Lord, and there is no other, besides me there is no God... Isaiah 45:5 ESV
So, we have a plural form of a noun that refers to a single entity--that is, God Himself. Genesis 1 identifies God and the Spirit of God in the first couple verses. As God's revelation of Himself progresses, we learn more about His nature. In the Old Testament, we see in Daniel one like "a son of man" approaching the Ancient of Days, a rock cut out of the mountain but not with human hands, a fourth person in the fiery furnace and other such things.
The first chapter of John is perhaps one of the clearest expressions of this:
In the beginning was the Word, and the Word was with God, and the Word was God. 2 He was in the beginning with God. John 1:1-2 ESV
Genesis told us that God and the Spirit of God were in the beginning. John tells us the Jesus Himself--the Word made flesh (v. 14) was also in the beginning as was also God.
Thus, the doctrine of the Trinity is what explains this. God was referring to Himself. The Father, Son and Spirit were all active in creation.