There are many options, If your using a SS from the game and need to cut the character out its a lot more work. for that you can either use the magnetic tool option, but that usually results in either cutting off a limb or detail by accident unless your really careful and the natural lighting was good, if its too dark, there are alot of factors that might be too much trouble. sometimes its just easier to paste the photo in a blank document and have you back ground layer set to transparent and then cut it out with the eraser tool. time consuming, but it ends up being the way you want it if you cant do it from another method listed below.
You can also cut it out using the mask tool, and set the edges to feather a little. that can work well if your going to the feathery signatures. if your not good at precise editing its very helpful.
If you are using model viewer, ( easiest option for fast signature bases) set your background in the viewer to an obnoxious color (or a grey if your careful) as if you were blue screening for a movie. once you go into your editor, if it has the magic wand tool use that and have the tolerance option low (10 and below should be more then enough) once its all outlined go to select, then inverse, then go to file and hit copy and paste it into a new empty document. character should be cut out all nice and clean for you to use. If for some reason there are still jagged edges you could always use the heal tool and just blur it a bit without messing up the main image. newer versions of photoshop actually have a refine edge option, but I don't know how well it works probably only as good as the base image itself.
you can also do that magic wand tool trick then go to contract in one of the top menus (sorry don't have photoshop in front of me for exact location) and tell it to go in a pixel or 2 and then go to select, then inverse and then gaussian blur those edges too. making duplicate layers and using blending modes and screens work gewd too. Mess about with the options they have, its the best way to learn those programs. Just make sure to back up the images as you go, layers are your friend. if using photoshop always save the layers unflattened as a .psd ('-')d