Step One: WHAT MAKES THE ICON THE ICON?
What about that character makes that character recognizable? Let's put it this way. Since Halloween was Monday think about if you were going to dress as this character for Halloween what are the first things that you would want to get for your costume. For Example, if you were to go as Harry Potter you would most likely draw a lightning scar and get a pair of glasses. For example, here is a snippet of a post you that will be coming soon of STEP BY STEP CHARACTER DRAWING with Harley Quinn from the new movie Suicide Squad.
At this point of the drawing, I had finished putting what is iconic about her face in. The first thing is her hair. Left side red, right side blue. The second thing that is very iconic is her necklace that says PUDDIN. I'm not a super realistic artist. By no means do my drawings look like photographs and that's okay. If you get the iconic items down than the drawing will "look like" the character.
Here is a drawing of some superheros I made them rally sloppy but you can probably tell who they are based on some of their iconic items.
Challenge: On your own draw some characters making the iconic elements clear but don't worry about the rest. I know that I have done a lot with super heroes but they are a great place to start because it id easy to find what is iconic. If you desire a warm up that is a little more of a challenge you can go for fairy tale characters.
Note: When you are just drawing a face remember that every face is unique. Look for what makes that face iconic if there is anything specific, (beauty mark, gold tooth, etc.) Sometimes it's not as obvious so you can just focus on these things. Face shape, Lip shape, eye shape, hair style, and than the color of all of the above.
Good luck on your drawing!