Clue (also known as Cluedo) is a board game about deduction. The game is highly thematic, with characters running around different rooms in a mansion and looking at various tiny weapons.
However, if you're just focused on how to win at Clue, most of the thematic stuff doesn't really matter. The weapon minis are irrelevant, and your attention should just be on getting information. Here are some basic strategy tips on how to do that.
(You should also review the basic rules of Clue.
Don't ask about cards you know your opponents are holding.
After you start by marking off all of your own cards, you'll want to learn about more cards you can mark off as soon as you can. When you make a suggestion, your goal is to get more information. If your opponents can show you the same card you've already seen, then you get no new information, and your turn has failed. The only cards that you have already marked off on your list that you should still ask about are your own cards since nobody else will be able to disprove them.
Eliminate one possibility every turn.
This is, of course, not always possible. But given that eliminating all false possibilities is your ultimate goal, the player who does this fastest has a huge advantage over the other players. To this end, you should ideally be making a suggestion every turn. Any turn where you do not make a suggestion is, essentially, a wasted turn.
Spend your time in rooms.
You can only make suggestions in rooms, so traveling on a roll of the dice should be seen as a last resort. When you enter a room, make a suggestion. If someone suggests you and drags you to a new room, make a suggestion there on your next turn.
Use the secret passages.
This lets you move from a room to another room, guaranteed, without having to risk rolling the dice.
That's two suggestions in a row that you get to make, without having to worry about bad luck stealing your opportunity.
If you haven't eliminated those two rooms after that, you can keep going back and forth between those two rooms until someone shows you one of those cards. Until they do, it's the most efficient way to gather information.
Try to learn about rooms whenever you can.
You can suggest any character or any weapon from anywhere on the board, but your room suggestions are limited by your location. For this reason, rooms can be the hardest thing to figure out, so you should learn about them whenever possible.
Spend time in any room you hold in your hand.
Not only will this let you learn more about the weapons and people, but you can use the unfair summons trick. If another player is about to reach a good room to make a suggestion (e.g. a corner room, or the likely murder room), you can make a suggestion about that player's character, which will drag their pawn back to your room. And if that player takes his next turn to make a suggestion in your room, you can simply show your room card.
Before playing, ask yourself how much work you want to do.
Clue can be played as a simple deduction game with the above tips, but if you're willing to write everything down and put in a lot of effort, you can gain additional information.
If you're desperate to win, you can write down each suggestion made, who showed a card to each suggester, who showed you each card, and which cards you have shown to each player. Doing this will be a lot of extra work. But it can give you a lot of benefits.
Don't give away any new information.
If you know which cards you have shown to each player, you can show them the same cards repeatedly to avoid giving away extra information. Never reveal a new card when you don't have to.
Use your knowledge about other players' hands to make new deductions.
If you know that Bob has the wrench card, and you have the Colonel Mustard card, and someone else shows a card to disprove the suggestion of "Colonel Mustard, in the Library, with the Wrench," you know that card must be the library.
Figure out what your opponents know.
If an opponent repeatedly uses the same item in suggestions, whether it's a location, weapon, or character, it probably means nobody else can disprove that item. If Suzy has made three suggestions in a row about the Revolver, chances are very good that the Revolver is either the murder weapon or in Suzy's hand.