Structured grids can be defined (since dumux 2.8 / dune 2.4) via the input file like follows:
[Grid] LowerLeft = 0 0 0 UpperRight = 4 5 6 Cells = 2 2 6 CellType = Simplex Refinement = 1 # optional
Note that Simplex is only available for grids supporting simplices. For multidomain applications the property GridParameterGroup can be set in each sub problem if you need to define different grids for the subdomains in the same input file.
Dgf grids can be set as usual with the default grid creator
[Grid] File = my.dgf