Using a blending/transfer mode like Add does exactly what it says: it adds the value of the upper pixels to the lower pixels, blending them together.
If your image has an alpha channel, it should sit on top without any blending modes required. If it doesn't, you may need to use a Key to remove the black from your image, or draw a mask around the image to remove the black.
As Andrew said, AE will handle normal transparencies/ Alpha channels just fine without resorting to blending modes. You just stack the layers on top of each other. The only problem you seem to have is that your imamge doesn't seem to have any transparency, so remove the black regions in Photoshop and save it as a PSD with layers where ther transparency is retained.
For a summary of the different ways that you can composite layers together, see this page: "Compositing and transparency overview and resources"
As the others have said, if your top image contains transparency information, then all the you have to do is put it on top of the other image with the Normal blending mode.
By the way, if you're new to After Effects, I recommend that you start here: "Getting started with After Effects"