Click on the “add filled zones” button. Then click on the PCB where you want the first corner of the zone. A dialog will open; here you can select your layer (Ground.Cu) and the net (GND). Then draw the other vertices of the zone.
Any through-hole component pin tied to GND in the schematic will automatically connect. For SMT, you will obviously need vias. Use the “select active layer” button to select the layers you want the via to connect (ie. top and Ground.CU)