Adam Neder always has good insights on Barth’s theology. The following from him gets into his elucidating what Christian Dogmatics is for Barth, and what it is based upon (the Word of God). This is all framed by Neder’s interrogation of Barth’s understanding of union with Christ theology or participatio Christi (a la Calvin i.e. ‘participation in Christ’). Neder writes:
Barth’s conception of dogmatics is grounded in his understanding of revelation, which governs his doctrine of participation in Christ as he articulates it in CD I/1. As an ecclesial activity, dogmatics proceeds from the Word of God and remains ever and solely accountable to it. Its task is free speech in obedient response to God’s speech, which is its sole criterion. Responsible to revelation alone, Christian theology hears and bears witness to the Word of God. Therefore, it does not attempt to justify itself through appeals to authorities external to revelation. Dogmatics is possible for one reason alone: because of the speaking and hearing of God’s Word. Thus, all attempts to ground dogmatics in anything other than the Word of God are in fact betrayals of revelation, since there is, by definition, no higher court of appeals on the basis of which revelation and theological speech about revelation might be justified. Genuine knowledge of God and speech about him are possible and actual because God makes them so. Christian theology presupposes this fact and makes no attempt to establish it. Prolegomena, therefore, is internal to dogmatics.
According to Barth, revelation is not merely the offering and acquisition of information. It is rational, to be sure, since it is the divine reason communicating with human reason. But since it is Dei loquentis persona, it is an event in which God establishes and orderly fellowship between himself and human beings. “God’s Word means God speaks,” and since it is God who speaks, to hear his Word is not simply to become aware of him, but to obediently acknowledge him as Lord. Thus revelation is inseparable from reconciliation. Moreover, knowledge of God is communion with God in Jesus Christ by the power of the Holy Spirit, and as such involves the death and resurrection of the human knower. To know God is to be joined to him in faith and obedience. The connection with participation in Christ is clear: “As God’s Word is spoken to man, it is in him and he is in the Word.” Barth refers to this union as a “mutual indwelling [Beieinanderseins] of the Word and man….”
Christian Dogmatics, for Barth, and for many of us, is something that is done in the sphere of the church; for its edification. But as Barth emphasizes (according to Neder) the church is simply the context within which dogmatic reflection is undertaken, what serves as regulative for it is the Word of God. Of course for Barth this means Jesus Christ, the eternal Logos (think threefold form of the Word); without Christ, without participation in Christ the church has no life blood and nothing to talk about—without Christ the church is a mute.
But we see, as Neder makes so clear in regard to Barth’s theology, that everything is contingent upon Jesus. Knowledge of God is not a static thing, but a personal reality, as such we must be in union with God in Christ personally if there is going to be any space for genuine knowledge of the true and living God. We can see how this would militate against a natural theology, as the sphere for knowing God is not in an abstract creation, but instead in the particular person of the eternal Son, Jesus Christ.
We can also see how Reformed Barth is. We see the lineaments and emphasis upon a theology of the Word develop early on in the Protestant Reformation; of course what is being referred to by the magisterial and post-reformers is Holy Scripture. This is indeed present for Barth, but again, as is typical he radicalizes things and focuses more dogmatically on Jesus as the Word, and then Scripture follows after; just as creation followers logically after the Creator.
If you haven’t been exposed to anything Barth yet, I think Neder offers a nice and intriguing way in for you.
 Adam Neder, Participation in Christ: An Entry into Karl Barth’s Church Dogmatics (Louisville/Kentucky: Westminster John Knox Press, 2009), 1.