Warning: Mysteries can be frustrating for your players. You want it to be complicated enough for them to think, but you don't want it so complicated they will get lost (which, depending on your group, can happen easier than you might think).
Now Let's start with the setup...
Who gets murdered?
This is the first and biggest clue. Learning about the victim will get the players the list of suspects.
Now the next bit is what will determine where the heroes should focus their investigation. If you complicate both of these then your players are far less likely to solve the mystery. There are too many distractions at the table and they may also draw wrong conclusions (more on that later).
How?
Strangled, Shot? If you want the source of the mystery to be about the "how" then keep the why simple. Examples of complicated "Hows" are things like the body is found inside a locked room, has been shot, and there is no sign of either gun or bullet. Typically once the heroes have figured out how, then it becomes clear only one suspect had the opportunity to pull it off.
Why?
This is for you to know and for your players to figure out. This becomes a complicated affair when it is apparent that every suspect had a motive. However in most traditional murder mysteries, the real motive is the one that isn't apparent until after the heroes start digging.
Proof
In order to prove a suspect is guilty, you need to be be able to prove three things: Motive, Means, and Opportunity.Motive - Did the suspect have a reason to murder the victim?
Means - Did the suspect have the knowledge and physical ability to commit the crime?
Opportunity - Was he able to commit the crime or does his alibi put him somewhere else at the time of the murder? Was he spotted in the area when the crime was committed?
If your players can accuse someone and can prove these things, then they have their criminal.
The Suspects
Your going to want to create a list of suspects and a Motive for each. In fact, List out Motive, Means, and Opportunity on a 3x5 card for each suspect. Only one suspect should have all three. The others should have one element that exonerates them such as a verifiable alibi, new information that makes there motive moot, or something that makes it physically or mentally impossible for them to have committed the crime.Clues
Keep it simple
Each clue should have meaning toward uncovering the culprit. Don't chain your clues in a specific order, where the heroes must find one which then gives them a clue to another, etc. If they miss a clue, then the chain is broken. Allow clues to be found and collected in any order.
Also, if the means to solving the mystery relies on the heroes finding all of the clues, then don't leave finding the clues down to a die roll. Die rolls fail.
Treat every clue as a means to narrow down the list of suspects. Remember the game Clue? It's not a bad model for what you are trying to do. If each clue narrows down the list of suspects, then each clue will tell the heroes where to focus their investigation until they finally zero in on their target.
GM Mistakes...
You are only human, and odds are you have only a week or two to come up with your mystery unlike a novelist who can take years crafting their story. Nevertheless your players may draw completely different conclusions from the clues you have left because they are vague, or because some other stimulus is leading them to the wrong conclusion.
If they pick the wrong suspect, but can make a convincing argument for Motive, Means, and Opportunity based on the clues you left...consider letting them be right. Honestly if they have thought their way through this game you have a victory as a gm. Many Mystery adventures I have seen tend to fall apart because the GM has made the clues too obscure, and the GM gets the heroes back on track by having them walk in on the villain doing something nefarious, thus triggering a fight scene. Basically the GM had to hand the villain over top the players on a silver platter.
