Whenever I paste an image into Photoshop, transparency becomes black

This is what I do:

1. Select the layer with transparency
   
2. Click on Menu item Layer, Layer Mask, From Transparency.
   

The transparency will be converted into a layer mask, that you can manipulate from there.

EDIT: in Photoshop CS5 or later.

Copy-Paste doesn't maintain transparency. Try saving file and then use Open File in Photoshop. AFAIK, Paint doesn't have the ability to save transparency enabled png files.