Firstly, A sincere appreciation means, appreciating something genuinely by heart. For example, If your friend has a good dressing sense and you really like that thing about him/ her, then complimenting him for that is so-called sincere appreciation. It’s just an example.
Secondly, If you found something interested and that catches your attention you should go and praise about that with the same excitement. Praising someone for their achievements, struggles, hard work will make a good impression of yours in their eyes.