Ahh, the wonderful world of layers. They seem scary at first, but once you get the hang you'll never go back.
On the layers palette, select the layer your logo is on and adjust the Opacity slider. It will look similar to the attached image.
To shrink it, select the layer and select Edit->Transform->Scale When you're done, either double click inside the area you just scaled, or click the checkmark button up on the main toolbar.
Next, you need to lean about masks...
Here's a page of tutorials. (leaf's, the surgeon's, and pacman's will tell you everything you need to know).
(BTW: I really like the logo!! )