I think I know what you're asking, but if I'm wrong let me know.
What you want to do is let the user download the app for free, let them use it for say 7 days, then require them to pay for the upgrade IAP (in app purchase) or prevent them using it?
If the above is correct there is one main problem that you're going to encounter. To track the date the user started using the app you will have to use something like a shared preference, an entry in a sql db or some local file etc... The only problem with all of these options is the user can erase the data and install the app again to use it free for another 7 days. The only way around this is to implement your own web registration service which I imagine would be a little too difficult.
The best way, assuming you're not too bothered about the people who will bypass it, is to capture the date/time when the app first starts and save it. Each time the app starts check if they have purchased the upgrade, if not check the current date/time against the stored value and if your trial period has elapsed, prompt them to buy the upgrade or close the app.