Here is how Barth summarizes the doctrine of providence:

The simple meaning of the doctrine of providence may thus be
summed up in the statement that in the act of creation God the
Creator as such has associated Himself with His creature as such as
the Lord of its history, and is faithful to it as such. God the Creator
co-exists with His creature, and so His creature exists under the presupposition, and its implied conditions, of the co-existence of its
Creator. God does this as His free will normative in its creation, and
His wisdom, goodness and power therein displayed, remain the same.
He does it as He is always to the creature the One He was when it
did not exist and came into being, as He continually acts as such
towards and with the creature which He has called to life, as He
sovereignly exercises His lordship over His work and possession in
new acts and revelations of His free will, wisdom, goodness and
power, and therefore as He causes the history of the creature to be
the history of His own glory. He does it as–far from leaving the
creature to itself and its own law or freedom, its dissatisfaction
or self-satisfaction–He causes it to share in His own glory, namely,
by the fact that it may serve Him in His immediate presence and
under His immediate guardianship and direction, thus fulfilling its
own meaning and purpose, having its own honour and existing to its
own joy. Hence whatever may take place in the history of the
creature, and however this may appear from the standpoint of its
own law and freedom, it never can nor will escape the lordship of its
Creator. Whatever occurs, whatever it does and whatever happens
to it, will take place not only in the sphere and on the ground of the
lordship of God, not only under a kind of oversight and final disposal
of God, and not only generally in His direct presence, but concretely,
in virtue of His directly effective will to preserve, under His direct
and superior cooperation and according to His immediate direction.
In this history, therefore, we need not expect turns and events which
have nothing to do with His lordship and are not directly in some
sense acts of His lordship. This Lord is never absent, passive, nonresponsible or impotent, but always present, active, responsible and
omnipotent. He is never dead, but always living; never sleeping,
but always awake; never uninterested, but always concerned;
never merely waiting in any respect, but even where He seems to
wait, even where He permits, always holding the initiative. In this
consists His co-existence with the creature. This is the range of the
fact that in the act of making it He has associated Himself with the
creature. He co-exists with it actively, in an action which never
ceases and does not leave any loopholes. And so the creature co-exists
with Him as the reality distinct from Him, and in its own appropriate
law and freedom, as He precedes it at every turn in His freedom of
action and with His work-He its Creator, who as such must no less
necessarily precede it than it must follow Him as His creature, and
be directly upheld by Him in its own existence, and stand under His
direct and superior co-ordination, and be directly ruled by Him.
Again, it is the majestic freedom of the Creator in face of His creature
which is as such the guarantee of the faithfulness and constancy with
which He is over and with it. Church Dogmatics III.3, p. 12-13.