In a murder mystery novel or stories alike, how do you give out hints and foreshadow key details without being obvious that those details are important yet if the readers read through it again after the plot twist, they will say something along the lines of "Oh! It's so obvious!"?
Trying to do this myself, I have two main strategies that work well for me.
Option one- Outline and use that to drop hints as you go along in your first run. This sets up all your hints, but if you decide to change something as you get there, it may invalidate one or more of your hints.
Option two- Write through first without the hints and then when you do a second draft, add in the hints. This way there is much less of a chance that you will change something to invalidate the earlier hints like option one, and your hints can be more specific because you know what will happen much more specifically than just outlining.
I've found one good way is to embed the plot critical item randomly into a list of items that aren't seemingly important (one of the best examples was the Locket in Harry Potter, which was first mentioned as a cursed item that was being disposed of in the beginning of Book 5. The fact that a locket was important was only brought up in Book 6 and Book 7 revealed that the important locket was the "garbage item" in book 5. In book 5, it was hidden from the reader's notice by including it in the middle of a list of other odd items that were being thrown out and it's only unusual feature is nobody could open it, which considering several other items were mildly dangerous, made readers focus away from that.).
Generally, the forshadowed details should be mentioned in a way that the reader wouldn't notice them until it's pointed out or they read a second time and see the item in a different light. One example of this is the staging used in "The Sixth Sense" that trick a first time audience into believing a different situation has occurred than what is really going on. The pattern is discussed in story, but at a point where it's not happening. Watching a second time with the ending in mind will recolor the original scene. Other examples of this include the nature of the two character's missions in Terminator 2. Today it's well known that the character played by Arnold is the good guy, but when the film was first released, both Arnold and Robert Patrick were delibertelty shot to obscure which was the hero and which was a villain. Even still, the twist was forshadowed by Patrick's character's introduction scene (while Arnold's character is once again beating up criminal jerks to get his clothing, as he did in the original, Patrick's character was different from the previous heroic archtype in the series in that he killed a cop to steal his gear AND while nude, lacked any scarring from the future war.). These were missed by the audience as Patrick's character acted a lot more human than Arnie... up until the reveal that Patrick is not human in the slightest.
There are 2 approaches:
Hide the clue in the background. As in the Harry Potter example that hszmv brought up, the first time the locket (and later another item) was mentioned, it appeared together with a bunch of other items and didn't really stand out as important compared to everything else that was going on.
Hide the clue in plain sight. Give a reason for why it appears in the scene and the reader won't attach any significance to it. According to "Chekhov's gun", if a gun appears over the mantelpiece in act 1, the reader expects it to be fired (or otherwise play a role) by the time the story is over. If the gun gets "fired" early, the reader is less likely to expect it to come up again later.
This doesn't just apply to objects but also to characters' actions and motivations. To bring up another example from Harry Potter, in The Chamber of Secrets, Ginny Weasley is acting strangely all year, which would make her a prime suspect, but the reader doesn't know her very well (she could just be weird) and her massive crush on Harry ends up explaining a lot of her behaviour.
Give reasons why the information or hint is important for a different reason. Disguise them, in fact.
Have the detective ask someone for the time, and the other character fishes out a pocket watch and gives it -- and only later do you realize that the detective actually was checking that the character was left (or right) handed.
The particular uses will depend on whether the detective is the point of view character, of course. The detective POV would require him to realize after the fact that it shows the man is left or right handed.