Why cannot I find any information about spanning tree for DAG ? I must be wrong somewhere.
Why focusing on dags and not general directed graphs? I think you should have a look at the directed minimum spanning tree problem, also known as the arborescence problem (PDF). The problem can be solved using the Chu-Liu/Edmonds algorithm. The wikipedia entry is not as clear as I was expecting, but it does have links to the original papers.
One generalization of a tree in a directed graph is an arborescence. It is a directed tree with all edges directed from parent to child.
The case for DAGs is trivial, which might be the reason you cannot find any dedicated information about them.
First, there must be a unique vertex $r$ of zero incoming degree, which is the root of the directed spanning tree (arborescence). (Otherwise no spanning tree can exist.)
Next, for each vertex $v \neq r$ choose a parent vertex $P(v)$ such that the $w(v, P(v))$ is minimal.
We chose $|V| - 1$ edges in a graph of $|V|$ vertices with no cycles, so thus chosen subset of edges forms a spanning tree $T$. Any other spanning tree, for each vertex $v \neq r$, must have a unique incoming edge $(v, Q(v))$. By our construction $w(v, P(v)) \leq w(v, Q(v))$. Summing over all $v \neq r$ we get that $T$ is minimal.