Brainstorming (and its variations) is probably the most well known and widely employed method for ideas generation.

Here are a couple of slightly different approaches.

Morphological analysis.

Consider the problem; ‘draw a dragon’

Then specify the parameters; Colour, Wings, Size, Defence.

Next list some variations for each parameter;

 

Now make random combinations by choosing one variation for each parameter;

A blue dragon with no wings which fits in your pocket and smells bad.

 

Now all you have to do is choose the best combination!

Try it yourself, do a morphological analysis for the problem “what shall we have for dinner tonight”.