You can move vertices with the help of the selection tool if you click on them (they should change color from black to blue to indicate that they have been selected).
You can delete vertices by right-clicking on them with the selection tool.
You can also delete your own polygons if you right-click on the polygon with the selection tool, then click on “remove selected object.”
Alternatively, you can edit polygons if you right-click on the polygon with the selection tool, then click on “add vertex.” This adds another vertex to your polygon if you need an additional one. The vertex appears on the edge closest to your click.