To get your PCs to move from one scene to the next logical scene, you need a series of connective tissues. These can come in the form of clues, rumors, lies, truths, and red herrings. Each one of these serves their own purpose and come from a variety of sources. Some of these will come from evidence found via investigative efforts. Some of these will come from conversations with NPCs. Some of these might even be sourced by overheard conversations.
At the end of each scene, the PCs should have some hint as to where to move next. Without these hints (or strong suggestions), your adventure will grind to a halt. If the party has gained a piece of connective tissue, but they’ve forgotten about it or downplayed its significance, it’s perfectly fine to remind them of their discoveries without pointing to the next scene directly.
Clues
Clues are generally found through investigation of a scene. These can be notes or letters left behind from the NPCs that occupied the space before the PCs barged in and took over the space. These can also be symbology, left over magical efforts, evidence of past encounters at that location, or deliberate hints left for the PCs to follow.
Let me delve into evidence for a moment. This can be your typical crime scene things like blood splatter, murder weapons, footprints, fingerprints, DNA, and the like. However, make sure each piece of evidence narrows the mystery a little bit. Footprints can clearly mark that the shoe is of a certain size, perhaps of a certain make, and might be scarred or contaminated in a certain way to narrow suspects. Likewise, DNA samples can be easy to gather, but take an excruciatingly long time to analyze. In your games, it’s fine for the PCs to pull some strings or use some advanced technology (or magic) to expedite the analysis to keep the game moving forward.
Rumors
Rumors are bits of information nested in truth the PCs receive from NPCs. The rumors don’t have to be totally true, but they need to be mostly true. If a rumor is mostly false, this falls into the arena of a red herring (read below) and may cause the players to make improper decisions on their next steps. Rumors are generally verbal in nature and can be couched in their deliver with some doubt or hesitancy to clearly show that the NPC giving the information is not absolutely certain of the details.
Lies
There will be times the PCs encounter NPCs that don’t want the PCs to succeed. This will lead to the NPC in question delivering an outright lie to the PCs to get them off track. If you decide to employ this approach of lying to the PCs, make sure the pathway down the wrong information is resolved quickly and with the obvious truth. You don’t want to waste precious time at the table with the PCs following a lie.
Truths
There will be times that an NPC or a note or a missive or a clue found will be the absolute truth. Hang a lantern on these facts and do your best to impose upon the PCs that these are truths, not rumors or lies. However, don’t tip your hand and allow them to 100% know that this information is to be trusted in their heart. If the PCs know the truth of the matter to be absolutely true, then they will close all doors to other options. This is rarely something you want. You want to keep the story options open. Also, dropping a 100% known truth on the party might feel a little like railroading to the players. While this is not always true, this is a feeling you want to avoid.
Red Herrings
Don’t.
Just don’t.
Red herrings are intentionally misleading sets of information that push a character (or group) down the wrong path. While this is perfectly acceptable (and even rewarding) in literature and movies, this can backfire on your game. This is because in literature a single author has total control over what the characters do and how they react to red herrings. In your games, you have no control over how the PCs act/react to red herrings you throw their way. This can completely derail your adventure by having the players treat a red herring as a truth and chasing that trail to waste endless hours of your game time.
In short, don’t blatantly lie to your PCs with incorrect information. You clearly can have an NPC with motivations to do so lie to your characters, but there should be some hints that the NPC is untrustworthy.
Gentle Suggestions
Lastly, you can have a meta-game or “out of game” conversation between you (the GM) and the players to remind them of clues, hints, and rumors that they’ve encountered thus far. There are plenty of times the players will lose track of information you’ve given them. This is especially true if you have a game that’s heavy on investigation and clue gathering. You don’t have to be blunt about it, but something along the lines of, “You seem to recall that George the Snitch dropped you a note about his arch enemy. Do you remember what that note said?” If they do, great. If not, you can gently guide them in the right direction.