Click with the selection tool on your polygon.
Then open via the Processing Toolbox the tool "Select by Location".
Select the Point Layer and your polygon layer with the selected polygon(s). Tick the Box "are within" and "Selected Features only" (this box you find under the drop down menu where you can select the polygon layer).
This will select all Points which are within your selected polygon. With the selection acitve, right click on your Point Layer in the Layer overview -> Export -> save selected features As
Here you can Pick .CSV as format and your desired location where to save the CSV file to.