This is the post #13 of the Calvin's Institutes summary series.
We must approach the doctrine of Trinity in humility, and listen to Scripture.
Scripture is God's revelation about Himself, and it teaches:
1. There is only one God.
2. There are three "Persons", and they are Father, Son, and Holy Spirit.
3. Each Person is truly and fully God.
4. Each Person is distinct from each other.
Even though the exact terms are not found in Scripture, those theological terms, such as, Trinity and Persons are helpful in teaching what Scripture teaches. They are also helpful in exposing and refuting those who deny what Scripture teaches on this topic. Nevertheless, we must be careful to understand what is actually taught in Scripture and what we mean by these terms. (Calvin seems to prefer the term, subsistence, over person, but retains the term, person.)
What we are trying to do with the doctrine of trinity is to express both the oneness and three-ness of God. There is only one God and He is not divided. And yet, there are certain three "persons" (actors/doers?) who are all fully God, yet, distinguished from each other by a special quality, and Scripture clearly reveals them as Father, Son, and Holy Spirit.
The Word mentioned in Scripture is God, and both OT and NT show that Christ is that divine Word, hence Christ is God. His divinity is also shown in what He has done and His miracles. The Spirit is also shown as God in His works, as well as other testimonies in Scripture (for example, 1. Christians are the temple of God. 2. The Holy Spirit dwells in Christians. 3. The Holy Spirit is the one that makes Christians the temple of God. 4. The Holy Spirit is, therefore, God. see 1 Cor 3:16–17, 1 Cor 6:19. For others, see Acts 5:3–4). And yet, there is only one God.
(This chapter was rather long and more difficult to understand. Although there's much more content I did not try to summarise here, it's probably better this way than to mis-express what is said on the doctrine of trinity.)