Sometimes we fail to remember what the Shorter Catechism says about the Godhead, that there are three divine persons, the same in substance, equal in power and glory. Each divine person fulfils specific roles and each of these roles is an activity that only God can do.
This means that the Spirit has divine attributes. The obvious one is found in his name, Holy Spirit. Moreover we can see that the Bible says he is eternal (Heb. 9:14); omniscient (1 Cor. 2:10-11); omnipresent (Ps. 139:7) and omnipotent (all power, such as what he displayed in his activity as Creator in Genesis 1).
With the other two divine persons he knows all the details of the eternal covenant and therefore uses his attributes to bring about the divine purpose. Their plan is an expression of their love, both within the Trinity and for those they determined to bring to full salvation. It is also an expression of their wisdom, of knowing what would be best for their glory.
We can think of what the Spirit did in the divine work of creation. Genesis 1:2 tells us that he was preparing the shapeless mass for a world that would be full of life. As far as caring for creation is concerned, Job 26:13, in some versions, informs us that the Lord beautifies the heavens by his Spirit. Elihu, when he was speaking to Job, acknowledged that 'The Spirit of God has made me, and the breath of the Almighty gives me life' (Job 33:4).So we can see that the Spirit is active in a creatorial manner in many different ways.
And then there is the divine activity of the Spirit in the salvation of sinners. His work of regeneration in a sinner, which is instantaneous, brings spiritual life into a previously dead heart and mind. Paul likens the greatness of this change in individuals to what took place at the beginning, at the onset of earth's story (2 Cor. 4:6). The Spirit teaches his people about their Saviour, about the benefits of salvation, about the reality of divine promises, and about the glory that is ahead (as Paul writes in Ephesians 1:13, the Spirit is the living earnest of the inheritance).
The obvious response to the fact that the Spirit is divine is that we should worship him with the Father and the Son. In our corporate worship we are reminded of the Spirit during baptisms and when we receive the Benediction. We should be grateful to him when he reveals to us the Father and the Son in a sermon, because no creature can do so. The Spirit is our divine helper.