So first, you need your image. I've chose
this one for the tutorial.

This method is easier to use on images that have... neat lines to follow? XD If that makes sense.. *is useless at explaining* You'll see.

So as I said up there, we'll be using the pen tool to extract our image, and the settings should be set as follows:
Now we can start drawing our path! I find it's easier if you zoom a little. Simply choose a place to start, and left click to place a point there. To draw a curve, just left click and HOLD it down as you move the cursor to fit the path around the curve. It might take a little practicing, but it's easy to get the hang of. It should look something like this:
Now, while holding the Alt key, we need to left click on the second point we made. This'll delete it and leave us to carry on from there, like so:
Now, you need to carry on with that method until you've created a path around the image that it is you want to extract, and when you're done, it'll look omething like this:
YAAY! Nearly done! Now you're ready to convert that path into a selection! It's easy peasy.
With your pen tool still selected you need to right click and choose the option 'make selection.' A toolbox will appear. Make sure the option 'Anti-Aliased' is checked. So I normally have the feather radius set to 1 pixel, but it's entirely up to you.
When you click OK, the path will convert itself into a selection!
Now using the move tool

, we can move just the part that has been selected, therefore separating our image from it's background and even placing it onto an even funkier background.