Errors are almost never entered directly into a spreadsheet but usually arise from problems which Gnumeric encounters during calculations. A list of errors with their meanings is presented in Section 5.2.5 ― Error Elements.
In an unusual case where it is needed, an error can be entered by hand like the entry of other elements. First the cell must be selected, then the error must be entered (e.g. #DIV/0!) and finally the Enter key must be pressed.