Study the classic monsters and think about what makes them popular and scary. Think about the traits that make them creatures the audience loves to hate. What characteristics of these classic monsters might you be able to work into your own creations?
Decide whether your monster is going to be based on a human being, such as Michael, Jason or Freddy. Or will your monster be something based on a world you've created? Make notes. Write down ideas for naming your monster, thoughts about the origin of your monster, and any characteristics essential to the way your monster behaves. Does your monster have a weakness, like many classic monsters do? Is your monster an alien, something supernatural, or something based on an urban legend?
Write an urban legend or a short story detailing the origin of your monster, then follow it up with sketches. You don't need to be an artist. The sketches can be rough and just basic enough to give you an idea what your monster will look like.
Borrow bits and pieces from established monsters and put your own twist on them. Many famous monsters share qualities and features. Yours can too, as long as you're careful not to rehash old monsters too much. The idea is to build upon the classic with originality.
Think about what scares you. Build your monster around your fears. A fictional monster based on real-life fears will be a more solid creation than some ambiguous or cliche creature. Your creature will be more believable. You might even consider basing your monster on real-world horrors like serial killers to add a touch of authenticity to your creation.