Android (or Java) example of webhook implementation is needed

Can you elaborate on what your scenario is? Webhooks are meant for server-side apps, and require a pre-registered URI where Dropbox can send notifications. Perhaps you actually mean /longpoll_delta?

I am using the Core API to access files on Dropbox from client on Android device. I would like to get notification about user's file changes when it happens. Does it possible by means of webhook or should I use old "/longpoll_delta way" to do it?

Yes, for a client-side app, such as on Android, you should use /longpoll_delta. The /longpoll_delta endpoint and webhooks both serve the same basic purpose, that is, low-latency notification of changes, but they're built for different scenarios, that is, client-side apps and server-side apps, respectively. In both cases, they just tell you when to call /delta.

I don't believe we have a sample of using /longpoll_delta on Android specifically, but I'll be sure to pass this along as a request.

That being the case, I recommend referring to the blog post and documentation:

https://www.dropbox.com/developers/core/docs#longpoll-delta
https://blogs.dropbox.com/developers/2013/11/low-latency-notification-of-dropbox-file-changes/

Thanks for clarification!