To duplicate a value, tap the cell and hold for a second, or to use a range, tap the first cell in the range and then tap and hold the last cell in the range. 

A pop over box will be presented, the cell or range will turn blue and there will be a menu shown with "Cut, Copy, More…"; tap "More…".

A menu with "Clear, Fill" will then be shown; tap "Fill".

The cell or range of cells will be surrounded by an orange border with "handles" in the middle of each edge. If a handle is tapped, and held, the border may then be dragged to cover the range of cells required.