How do you see patterns on the GMAT?

Great question!

There's a big difference between memorizing rules/formulas and applying those rules in creative ways.
I'd say it's analogous to memorizing a joke and writing a joke.

Given that we're talking about creativity here, I'm not going to suggest that all you need to do is follow/memorize a few strategies, and then you'll possess creative problem-solving skills

Instead, I have two suggestions.
1) Read up on George Polya and what he has to say about problem solving (from an educational standpoint, he's the king)
2) Carefully review the responses in the BTG math forums. Here, you'll see some great, creative problem solving at work. The more creative problem solving you see, the better equipped you'll become.

I hope that helps.

Cheers,
Brent