Some of these signs can be easily observed by reflecting and by paying attention to Islamic texts.
Here, three signs of God’s oneness are discussed:
1- Sending prophets
One reason why God is one is what Imam Ali (AS) has said in Letter 31 of Nahj a-Balagha: “Had there been any other god, besides the One, he; would have also sent his messengers and prophets to show us the sigs of his power.”
2- God’s infinity
If there were two gods and the universe had two sources of power, it would mean either both of them are limited, and consequently not god because limited power will ultimately be destroyed, or they are both unlimited would mean they are not two but are one.
An example would clarify the issue. If you tell an architect to build you a house that has an unlimited area, he would certainly not build more than one house, because there would be no land remaining for any other house.
3- Coherence in universe
If there were another god or other gods in addition of the One God, the universe would certainly move to destruction. “Had there been other deities in the heavens and the earth besides God, both the heavens and the earth would have been destroyed. God, the Lord of the Throne, is too Glorious to be as they think He is.” (Verse 22 of Surah Al-Anbiya)