Only table owner(s) can add, configure, remove or rearrange columns.
Adding a column is very easy; just click on the + icon between two columns or on the top right of the table:
If you click on the gear icon on the header of any column, the column menu offers options to delete the column, empty its values, move it, apply a filter or sort the rows:
The Clear column values function is not available on mandatory or automatic columns.
Most other options only appear if you own the table.