I've ran a mobile app development company for the last 6 years. My team has developed many apps for entrepreneurs and startups, I am frequently asked this question.

First understand that startups are 10% idea and 80% execution. With limited budget and/or time, I would suggest to do your best to define the requirements of your app idea, mock up the screens to best of your ability (see: basamiq.com or mockingbot.com).

Next, after your idea is minimally defined, bounce it off of as many people (that are not friends or family, they are biased) as you can to determine if your solution to your perceived problem works.

In terms of getting investors, start working on a 10-12 pitch deck. See Guy Kawasaki's template: http://guykawasaki.com/the-only-10-slides-you-need-in-your-pitch/

Good luck!