I used to write for Harlequin Intrigue. Mysteries were my thing so I know a little about hiding clues. I'll share what I discovered by trial and error and what I've learned from research. Remember, clues aren't just needed for mysteries. I think all books have need for clues. Maybe the hero in a romance novel is hiding a secret from his girlfriend. She needs to find a clue. I think all genres need some sort of mystery whether it's about the characters or some event. So here are some tips on keeping the clues from jumping out and being obvious to your reader.
1. Bury Clues in Lists: This is something I've used in the past. I remember one book where I wanted to put a clue in a drawer but didn't want anyone to notice until later. So I had the character go through the drawer and I listed the items. None of them seemed important at the time. One, however, was extremely important.
2. Hide Clues in Dialogue: This is a good one. Write a seemingly innocent conversation. It seems mundane to the reader, but there is a clue if they read it carefully enough.
3. Distract the Reader with Action: It's a fact that readers get distracted by action. They are living in the moment. There eyes are going faster, heart beating, and they just might miss a clue if you carefully place one here.
4. Have a Hair-brained Character Figure it Out: If you have a character who talks a lot of nonsense, the reader won't see them as reliable. So have them hit the nail on the head, just once. Have them say something incredibly brilliant in such a way that the reader won't believe it... until later.
5. Place the Clue in a Joke: This is sort of like the above rule. If a character is making a joke of the truth, the reader probably won't believe it. J.K. Rowling used this one in Harry Potter. It was brilliant. She had Dumbledore joke that Harry and Hermonie couldn't possibly be in two places at once when that was exactly what was happening.
6. Point the Finger at the Bad Guy: This method was used in the first Scream movie. They made Billy look guilty and then cleared him. Once you clear the bad guy no one will suspect them later. Smart move.
I'm sure there are other clever ways to hide clues. These are some of my favorites. As a writer you want to place the clues around so the reader won't fill cheated later, but you don't want them to figure it out too easily. They won't buy your books anymore. Readers want to play detective and sometimes they want to figure out the mystery before the detective does, but not too soon. Happy writing!