Where can we find dialogues related to anime?
Depending on how you get your anime fix...

DVD/BD

In my experience, while most Japanese DVDs do not have subtitles in Japanese, some do. It is usually easier to find movies than TV series subtitled though.

Streaming

Online streaming services such as Viki have some Japanese shows with Japanese subtitles. Most of them non-animated TV dramas though. But perhaps you can find some anime with the services available to you. Or you could watch a TV drama based on a manga/anime... (Below a screenshot from the Sherlock Holmes puppet show on Viki.)



Other online resources

Around the millennium shift some websites offered fan translations of Japan-only anime shows. That is, you could try to get the Japanese VHS/DVD and follow along with the translated script. If I remember correctly at least one of those websites had the Japanese script as well. This was before the fansubs found a home online. Maybe something similar exists today. I am not aware of any such resources though.