I don't have this pack but it appears to be a set of layered photoshop files, presumably with one graphic (i.e. mane, tail, etc.) per layer.

I assume you have an image into which you want to insert a graphic from this pack. Open the relevant pack file, then click on the layer with the required graphic. Assuming the graphic is on an otherwise transparent layer, all you need to do is select the move tool and drag the layer from the pack file onto your image. This will automatically create a new layer in your image with the mane (or whatever) in it.

That should be all you need to do, unless the graphic isn't on a transparent base. In which case it becomes a bit more... challenging.

Steve