Begin by drawing nodes to make a polygon, the last nodes needs to intersect the 1st node. Double-click to complete polygon. After you complete the polygon if you need to straighten out the lines you can use the shortcut ‘Q’.
In JOSM, use the Select tool (shortcut=S) to select objects. Be aware that you can select both nodes and edges. Often you just want to select a building or a highway by just clicking on the edge to modify the tags.