How to show that every connected graph has a spanning tree, working from the graph "down" I am confused about how to approach this. It says:

Show that every connected graph has a spanning tree. It's possible to
  find a proof that starts with the graph and works "down" towards the
  spanning tree.

I was told that a proof by contradiction may work, but I'm not seeing how to use it. Is there a visual, drawing-type of proof?
I appreciate any tips or advice.

Let G be a simple connected graph, if G has no cycle, then G is the spaning tree of itself. If G has cycles, remove one edge from each cycle,the resulting graph will be a spanning tree.
