I'm trying to place a logo on the bottom right corner of the image in the following link, but I'm not sure how. The plastic casing is a phong material and I'd like to have the logo there. Is there a way to do this so it doesn't look like a sticker waas put on with a while box around?
Sure, this can be done with the correct settings on your place2dTexture node. Turn down Coverage so your logo image appears small, then change Translate and Rotate attributes to put it where you want it on the object.
The step that some people miss after turning down Coverage is to set the Default Color of the file node to the colour that you want the rest of the surface (i.e. where there's no logo) to be. If you've got another texture creating the colour of the material, you can just connect that texture into the Default Color attribute of your file node and you should be done!
If your logo is an odd shape (not rectangular) AND the rest of the material needs to have a texture applied to it (so you can't just colour in the background the same colour in Photoshop) and therefore can't be 'cut out' easily, then you will be looking at going the Stencil or Layered Texture route.