Photoshop is a very full featured program for photoediting. The effects achieved here were done by:
Opening an existing .gif file (the sea monster).
Select the marquee tool and surround the portion of the .gif you see here.
(The soft edge was created by setting the feather value (found on a pop-up menu) at about 10 pixels.) BTW--feathering won't be apparent until you paste the selection into a new layer or file.
Copy the selection to the clipboard.
Create a new file.
Paste in the selected portion of the image.
Open another .gif file (the alien).
Select the portion of the file you see.
Return to the sea monster file.
Create a new layer from the LAYER menu.
Paste the alien in.
Click on the background layer to make it active.
Add some background effects under Effects menu, FILL command. This was achieved by using the DISSOLVE option at about 40%. Several colors were added this way.
The other graphics were added the same way--some with rectangular feathered selections, some with elliptical feathered selections. Play around!
The other cool thing Photoshop can do is make layers more or less transparent (called opacity). By using something less than 100% opacity, you can have objects "show through" from behind things.
The final step is to save the file into a .gif format by using FILE/EXPORT as gif 89a. Then put the image into your page as normal.
If you like these effects, a lot of people use Paint Shop Pro (from JASC) to do similar things. The program doesn't have quite as many editing options, but then, it's only $79.00, or there's also a "lite" version which can be downloaded for free at http://www.jasc.com.