Getting your mobile app found in the app store?

I'm creating a my first mobile app. What are some app store optimization tactics to get your app discovered?

How can I stand out from the crowd in my category and potentially get to the top paid apps list?

In reverse order:

Assuming you mean the Apple App Store, then getting to the top of the paid apps list is achieved by selling "a lot" of your app. "A lot" is a term relative to the competition in the category/list you want to be at the top of.

Standing out - obviously having good visuals is no longer option, but a minimum requirement. Having good descriptive and persuasive text is necessary. Having an app that people want is really the best advantage.

I'd suggest that you think about your target audience and figure out where they are likely to discover you - it might not be in the App Store at all.