I would like to know which is the difference between 詳しい and 細かい？
When do I use each one?
Thank you so much in advance!
In the first place, 細かい can be used for anything that you conceive to have fine texture or grain size (literally or figuratively). 詳しい is only for information.
When you use them on the quality of information, you may be confused because both can be translated as detailed. But the basic difference is that: 詳しい means rich in content and not necessarily minute in scale, while 細かい still describes how narrow the scope is, not necessarily how dense the content is.
Imagine a digital image, where 詳しい is its resolution (amount of pixels), and 細かい is zoom level. In some systems such as Google Earth, the more you zoom in (細かくする), the clearer the image becomes (詳しくなる). But however you zoom into a particular section of an ordinary image, you are not able to get extra information, just those bigger squares (which, in turn help designers make the image pixel-perfect).
マナーに詳しい人 who knows a lot about manners
マナーに細かい人 who is particular about manners
When you say 詳しいこと, it means additional information that can fill up your incomplete understanding at this point. 細かいこと, on the other hand, some minor detail that don't change the bigger picture, which may be unimportant, or may be crucial while you thrash out a contract.
詳しい話が聞きたい I'd like to know more of it.
細かい話が聞きたい I'd like to know the specifics.
The main difference I think is that 細かい can be to describe the delicateness/fineness/smallness, for example for physical objects, but 詳しい cannot. Here are some examples:
細かい砂 (fine grained sand)
肩が細かく震える (shoulders shook slightly)
細かい金 (small coins/money)
細かい違い (small difference)
Another main difference is that 細かい can be used for negative impressions, whereas 詳しい cannot.
細かい事まで口を出す (say things to the point of being too detailed)
金に細かい (stingy with money)
詳しい is most often used about knowledge
京都に詳しい人 (knowledgeable about kyoto)
詳しい調査を行う (perform a detailed investigation)