You access these basic objects through the Toolbox, which you call with SPACE or SHIFT-A the difference between these two is that SHIFT-A places the highlighted menu-entry in the add menu, SPACE shows always the last selected option. With the mouse you can call the Toolbox by clicking the Toolbox-icon at the upper right corner of the Blender-screen.
Set Blender to his default scene by pressing CTRL-X , remember that this action will delete your current scene, so save if you want to keep it. Bring the mouse-cursor over a 3DWIndow and press SHIFT-A , the Toolbox with activated ADD-menu pops up.
Next click with LMB on the menu-entry "MESH", the menu changes and shows now the different possibilities for adding mesh-objects.
Select "Plane", the Toolbox disappears and a Plane shows up at the 3DCursor. We are currently in the EditMode, where we can edit the shape of the mesh himself. Now press TAB to leave EditMode, the Plane becomes purple in the 3DWindow.
It is most likely that this Plane is exactly above the default Plane so press GKEY to enter the grab mode, move the plane with the mouse a bit off and confirm the new position with a LMB -klick.
Now we are going to add a more interesting object. Press SHIFT-A again, then choose "UVSphere" from the "MESH" section.
In this case the Sphere doesn´t appear at one, but Blender asks you for a few more information. The "Segment" and "Rings" input fields are asking for the resolution of the Sphere we are going to create. For this just klick "OK" or press RETURN . Again leave EditMode, and move the Sphere to a position you like.
Add a few more objects from the Toolbox with the procedures described above. Then use the middle mouse to rotate the view and explore the objects you have just created. Use the MMB together with SHIFT and CTRL to translate and zoom the view. Use a perspective view (PAD5 ) to get a more 3D look.
Especially notice how the objects are composed out of the single edges. Use the EditMode (TAB ) to explore the vertices of a selected object.
Press ZKEY to switch on and off filled objects in the 3DWindow.