It depends on the how much effects you would like to add.
For graphic design you can use Photoshop but if may take you a while to learn how to use it if you are not familiar. If you only want to add basic effects you can try any of these tools depending on what type of effect you need.
1. Portrait Painter Software
2. GIMP Image Manipulation
3. Teorex Inpaint
I started doing some special effects with the very first paint shop pro. It was a huge learning curve, but I was able to play around with the program some and had some fun.
If you are serious about really doing trick photography and great special effects the easy way, then you need a program.