<lightning:datatable
                    keyField="id"
                    data="{! v.data }"
                    columns="{! v.columns }"
                    hideCheckboxColumn="true"/>

<lightning:button variant="brand" label="Add Row" title="Add Row"
                  onclick="{! c.addRow }" />

addRow : function (cmp, event, helper) {

    // this fetches the existing data as rendered in datatable
    var myData = cmp.get("v.data");

    // now push a new empty row in the array retrieved
    myData.push(
        {
            myfield1: "",
            myfield2: ""
         }
    );

    // now add the new array back to the attribute, so that it reflects on the component
    cmp.set("v.data", myData);
},