Tinkercad is a very fast and simple way to start 3D modeling, lowering the barrier to entry with it's intuitive austerity. The refined interface has no clutter with (currently) only four basic tools: Add, Sub, Workplane and Measure on the left side with basic navigation on the right.
With the limited tool-set you are not about to start modeling complex organic forms but if you wanted to teach somebody the fundamentals of solid 3D modeling you would be hard pressed to find a simpler starting point: Extrude a form, Subtract from form, repeat process, 3D print (with Shapeways .
Tinkercad uses WebGL and is currently supported in Firefox and Chrome but apart from that is operating system agnostic, requires no downloads, all you need to do is register and you are ready to start 3D modeling.
Once you are logged in you can start playing around with the controls or try one of there 'Quests' to help orientate you with the tools, you can of course then upload your design to 3D print with Shapeways, direct from your browser.