Doctrine on the Holy Spirit is difficult to speak about, because it defies normal theo-logical definition. All activity of God in earthly or churchly life is by the Spirit. Without the Spirit, the Bible would be a closed book to us, the sacraments would be mere ritual, our lives would not be inspired to change and redirection and growth in Christ, our churches would fail to be a fellowship and would not be knit together as a body. In a sense, we talk around the Spirit rather than on the Spirit; we describe the effects but not the nature. Yet, since we can't comprehend any of God's work on earth without the Spirit, we cannot engage in theo-logy without talking theo-illogically about the Spirit.
The Spirit does not bear witness of itself but of Christ - which of course makes the Spirit even harder to understand. The Spirit does not physically do anything. All action happens through the physical world's beings and activities. So it's easy to mistake the Spirit's work for our own work, or that of other people or of nature or science or society -- and vice versa. Easy, but crucially wrong. Barth described the Spirit as "the subjective reality of revelation".
The early Eastern Orthodox teachers put it this way: the 'face' of the Father is revealed by the Son; the 'face' of the Son is revealed by the Spirit. Notice: there is no Person who reveals to us the 'face' of the Spirit. The shape of the Spirit's 'face' is recognizable only by way of the unseen Spirit itself, working through the Scriptures in revealing Jesus. Even the Scriptural witness to a vigorous and powerful entity is not direct, visible, or clear. The Spirit, after all, is who makes the Bible so useful in revealing faith matters. The Scriptural witness is to the presence, activity, and effect of the Spirit -- a second-hand report of the 'face' as seen in a fog bank. If we are to look in Scripture for the Spirit's 'face', it's best found in the same source that best reveals the Father -- Jesus. For it is Jesus who is God-with-us, God at His most tangible and most detailed. Even that, however, is indirect, for Jesus is not the same Person as the Spirit. This leaves the followers, the 'church', or 'Body', of Christ, formed by the Spirit -- but that comes in countless shapes, and is often far from living in a way that reflects the Triune God. Thus, the mist remains. We are left to probe, try, test, ponder, and ultimately just live in the mystery of the Spirit.