It's not that you have to "apply" a short circuit, it's that you have to be able to see when something is short circuited. This means the same node appears on both sides of a circuit element. What I do when I see something like this is mentally color in each node a different color, like this:

As you can see by coloring in the nodes, the 7-ohm resistor in the first one is short circuited (all of the current will go through the wire to the right of it because 7 is infinitely greater than 0, ratio-wise). In the second one, the 5-ohm resistor on the right is the one short-circuited.
After that, it might help to redraw the circuit so everything flows from left to right instead of having things that go up and down like they are now. At least, it works better for me to visualize it and make sure I don't accidentally say some things are in series when they should be in parallel. I've drawn out #1 for you, so you can draw out #2 and solve it too.

In the future though, this sounds like it should be in the Homework sub-forum.
Edit: If you want to check your work against answers, the resistance of the first circuit is 2 ohms, and the resistance of the second circuit is 6.5 ohms.
This post was edited by bentherdonethat on Dec 6 2010 10:29am