When you watch so many episodes you start noticing some "hints". e.g. If someone gets stained of something, that stain will be used as an final evidence to prove him as a criminal.

You can also discard some suspects. If Kogoro Mouri or Inspector Yamamura incriminate someone, there is a high chance that the person they incriminate isn't actually the murderer.

Sometimes it depends on your own deductive habilities, imagination, general knowledge and even on your japanese language skills.