There isn't anything to cut out, though I'm not sure what format you're working with.
These are pcx's which have been extracted from an sff file. The tools are sprmaker, SFFextract, and a front-end for SFFextract.The pcxs are then renamed as you say, into a layer set. (assuming you don't plan to change the sprites in any way)
They can also be saved as psds, saving a step.
I wil of course mention that the sprite authors ask to be credited on their sites, so for me it's either rebuild them or don't use them without at least a repaint.
If you mean something like using sprite sheets, or screenshots, well that's kind of primitive compared to this method. I get several hundred images from a sprite, and I can make them from scratch, etc.
Edit:
I'm not shooting for an easy way to cut something out, etc. But thanks, really. I'd rather stick w/ the "learn how they do that" method.