How do I power Redstone through a block?

I have seen this in YouTube videos: a person places a Redstone Torch on the wall like in the picture, and it activates a circuit. No matter how many layouts I have tried I can't seems to get a power output on the other side. My question is, how can I power Redstone on the other side of this stone block?

What I imagine is happening is something like this. When the Redstone Torch (highlighted by my cursor) is placed...

...it powers the orange wool block above it. On top of this wool block is Redstone Dust, which in turn becomes powered.

You can then transmit this signal to wherever you want. In this case, I'm powering the Iron Door.

To answer the question in the title, these are the ways to energize a block, allowing passing signals through walls:

• A redstone torch below the block. (This is what is happening in the particular example; Kevin Y has given a fine illustration of the situation.)
• A redstone repeater beside the block, facing it.
• Redstone dust on the block.

Each energized block will power redstone dust beside or on it.

Note that the rules for energizing solid blocks are different from the rules for energizing redstone dust and should be considered separately.