Developers can choose whether to allow a trial of 1, 7 or 30 days, or to disallow trials all together, on a per-app basis. For those apps that allow trials, the App Store would show a “Try for 7 days” button alongside “Buy app”.
If you install the trial app, it gets flagged with a “Trial” flag over the icon, in a similar way to the “New” flag that was introduced in iOS 6.
It’s been debated many times over whether or not a “trial” period for apps would be a good idea. Something like this would effectively kill the “lite” app model that we’ve seen since the App Store’s origin. Is this something you would like to see? If so, what benefits does it have over the current system?