You can create a new shapefile layer manually.
On the left side, click on New Shapefile Layer
Select Point, Line or Polygon
Select a CRS
Create new fields (columns) if necessary
Click on OK
Give the new shapefile a name and save it
Click on OK again
Put the new layer at the top of the Edit mode (yellow pencil)
Add new elements manually to the shapefile by drawing them, giving them an ID and, if relevant, other additional values
When you are ready, click on the yellow pencil again to leave the Edit mode and save the changes in the new Shapefile.