Open the object you want to move to a different background. In this case I'm going to use Sonic the Hedgehog

Now open the background that you want the object above to be moved onto. In this case I choose the image on the right.

Go back to the object(Sonic) and take the Magic Wand (Match Mode: RGB Value | Tolerance: 0 | Feather: 0 | Sample Merged: Unchecked). Using the magic wand select the background your object is in currently.

Go to Selections--> Invert and your object should be selected. Now go to Selections--> Modify--> Feather, for the number of pixels to feather enter roughly 5. Increasing this number will make a bigger white border later on and decreasing will make a smaller border around your image. Then once you've done that right click on your image and click Copy(CTRL + C).

Go to the image you want to paste your object(Sonic) on. Right click and click Paste as New Selection, now you will see that you have your object on your cursor. Move your object to where you want it but before you click take note of the number on the bottom left hand corner, write this number down somewhere. Then click to put your object down.

If you would like your object to have a glowish sort of effect then right click again and click Paste as New Selection. Now remember that number I told you to write down before? Well get the numbers and move your cursor around until you find that exact same number in the bottom left hand corner. then click again to release the object. Do this as many times as you desire until you get the right amount of glow.