Associate an event double click on a QTableWidget to a slot and get the row

The doubleClick signal already returns an instance QModelIndex from which you can obtain without problems the index of the row with QModelIndex.row() , the problem is that the signature of your slots and its call are incorrect in principle. An instance method must always receive self as the first argument , in addition self is passed automatically , you should not pass it explicitly when calling.

On the other hand, when calling a defined method def metodo(self, arg1) you must do it using self.metodo(arg1) , not using metodo(self, arg1) (in any case it would be NombreDeLaClase.metodo(self, arg1) which is what self.metodo(arg1) actually does)

Connect the signal with:

tableWidget.doubleClicked.connect(self.on_click) 

Your slot may look like this:

# from PyQt5 import QtCore

@QtCore.pyqtSlot(QtCore.QModelIndex)
def on_click(self, index):
    row = index.row()
    column = index.column()
    print(row, column)

With the button happens the same, do not use lambda to try to pass the instance of the class, simply:

toolButton.clicked.connect(self.exportar)

As long as exportar and on_click are of course instance methods of the same class that is the Tabla method. I leave a reproducible example based on your code anyway:

import sys
from PyQt5 import QtCore, QtWidgets 



class Example(QtWidgets.QDialog):

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        self.mainLayout = QtWidgets.QGridLayout()
        self.setLayout(self.mainLayout)
        self.columnas = ["Columna 1", "Columna 2"]
        self.listaDatos = [["A", "B"],["C", "D"]]  
        self.tabla()        


    def tabla(self):
        #Boton de exportar a excel
        self.toolButton = QtWidgets.QToolButton()
        self.toolButton.clicked.connect(self.exportar)   # <<<<<<<<<<<<<<<<<<<<<<<
        #Tabla
        self.table = QtWidgets.QTableView()
        self.table.setObjectName("table")

        self.tableWidget = QtWidgets.QTableWidget()
        self.tableWidget.setObjectName("tableWidget")
        self.tableWidget.setColumnCount(len(self.columnas))
        self.tableWidget.setRowCount(len(self.listaDatos))

        #Colocamos la cabecera
        self.tableWidget.setHorizontalHeaderLabels(self.columnas)
        header_view = self.tableWidget.horizontalHeader()
        idx = header_view.count() - 1
        header_view.setSectionResizeMode(idx, QtWidgets.QHeaderView.ResizeToContents)

        #Colocamos los datos
        for fila, lista in enumerate(self.listaDatos):
            for columna, elemento in enumerate(lista):
                self.tableWidget.setItem(fila, columna,
                                         QtWidgets.QTableWidgetItem(elemento)
                                         )
        # Evento
        self.tableWidget.doubleClicked.connect(self.on_click)  # <<<<<<<<<<<<<<

        #Layout
        self.mainLayout.addWidget(self.tableWidget, 7, 0, 5, 7)
        self.mainLayout.addWidget(self.toolButton, 6, 5, 1, 1, QtCore.Qt.AlignRight)


    #Metodo asociado al evento de hacer doble click sobre una fila de la tabla 
    @QtCore.pyqtSlot(QtCore.QModelIndex)
    def on_click(self, index):
        row = index.row()
        column = index.column()
        print(row, column)


    @QtCore.pyqtSlot()
    def exportar(self):
        '''
        A modo de ejemplo solo imprime el contenido de la tabla
        en forma de csv
        '''
        print("Exportando tabla:")
        for row in range(self.tableWidget.rowCount()):
            print(",".join(self.tableWidget.item(row, column).text()
                for column in range(self.tableWidget.columnCount())))


if __name__ == "__main__":
    app = QtWidgets.QApplication(sys.argv)
    dialog = Example()
    dialog.exec_()

Depending on what you want to finally get there are a couple of other signals that could help you:

• itemDoubleClicked(item: QTableWidgetItem)

  self.tableWidget.itemDoubleClicked.connect(self.on_click)
  
  @QtCore.pyqtSlot(QtWidgets.QTableWidgetItem)
  def on_click(self, item):
      print(item.text())
  

• cellDoubleClicked(row: int, column: int)

  self.tableWidget.cellDoubleClicked.connect(self.on_click)
  
  @QtCore.pyqtSlot(int, int)
  def on_click(self, row, column):
      print(row, column)
  

For headers you also have similar signals, such as sectionDoubleClicked(logicalIndex: int) to get the index the row if you double click on a section of the vertical header:

self.tableWidget.verticalHeader().sectionDoubleClicked.connect(self.on_hheader_click)

@QtCore.pyqtSlot(int)
def on_hheader_click(self, index):
    print(index)