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Programmatically Insert a Cell in a Notebook

After the Cell Being Evaluated...

Insert an input cell after the cell that is being evaluated:

Insert both a text cell and an input cell:

At the Current Selection...

Make a button that inserts a text cell at the current selection:

Wolfram Language code: Button["Insert Cell", NotebookWrite[InputNotebook[], Cell["Hello!", "Text"]]]

Use the button to insert a cell at the current selection:

Notes

Wrap the first argument of ExpressionCell with Defer to prevent it from evaluating:
Wolfram Language code: CellPrint[ExpressionCell[Defer[2 + 2], "Input"]]
Wolfram Language code: 2 + 2
NotebookWrite is a low-level function that requires low-level representations of typeset cells, typically constructed using Cell, BoxData and ToBoxes:
Wolfram Language code: NotebookWrite[InputNotebook[], Cell[BoxData[ToBoxes[{1, 2, 3}]], "Input"]]
Wolfram Language code: {1, 2, 3}