To begin with, it's the Keeper who knows the who, what and how before the scenario starts. The players then have their inquisitive characters discover the clues that help to solve the mystery featured in the scenario. The Keeper's scenario notes are not a story - the story occurs as the players bring life to the scenario through their character actions.
Clues
Trail of Cthulhu scenarios are not about finding clues. They're about interpreting the clues you do find.
Finding the clues in ToC is pretty automatic. Then the fun begins, when you try to put the components of the puzzle together. All you as the player have to do is:
1. Get your investigator into a scene where relevant information can be gathered.
2. Have the right ability to discover the clue.
3. Tell the Keeper that you're using that ability.
Here are three examples of how you can do this without overtly bringing in game terms and breaking the mood of your post:
Viscount Exeter draws on his knowledge of the occult to see if he can recall what the symbol scrawled on the wall means.
Alternatively:
Viscount Exeter buys the already inebriated Dr Wait another drink and spends the next few minutes casually prompting him to reveal the results of the blood tests.
Spoiler:
Or finally:
Viscount Exeter takes an evening stroll around the hotel. As he does so, he looks out for any strange architectural features in the buildings in the neighbourhood that may denote an occult leaning on the part of the occupants.
Spoiler:
Clues are normally found by the player with the highest ability score related to finding that clue. However, any character with the necessary abilities will find a clue if they specifically state they are using it in the right way. For example, "Viscount Hilary ignores the body on the floor, moving instead to examine area around the broken window where the intruder gained access".
Spends and Benefits
Certain clues allow you to gain special benefits by 'spending' either one or two points from the relevant investigative ability 'pool' (your character's numerical rating for that ability).
Sometimes the Keeper will ask if players if they want to spend, sometimes it's the players who request a spend. Either way, any benefits or information gained will add flavour to the scenario but spends aren't required to actually solve the case or move the investigation on. Usually a spend will allow something to take less time than normal, or succeed in that ability in a more extravagant manner, or perhaps grant benefits useful later in the scenario.