Of course you'll get the most fun if you figure everything out by yourself, so I recommend to use this walkthrough only if you have serious difficulties and can't progress even if you rested from the game and then returned to it more than once, but still can't find the solution.
After Melissa wakes up, you begin playing at the open front door of the Abandoned Mansion. From here, look around, explore the place, enjoy the atmosphere of your surroundings and cutscenes that you will find. Searching for something interactive is very easy: when you approach such object, an on-screen prompt will appear, inviting you to press "1" key to interact.
Eventually, you will find coupler on the shelves in the boxroom, and valve in the pile of snow in the yard. Go to the basement, stairwell there is located right under the stairs to second floor. Use the coupler to open the electric panel, and connect the wires.
You can use the valve to unlock the pipework, and redirect the steam now or postpone it for later. You didn't play the Game yet, and if you die there, you'll have to redirect it again. Considering it, you might choose to postpone.
When the wires are connected, lights on the second floor are now working, and therefore Melissa isn't afraid of going there.
Explore the second floor. As you can see, only two rooms are opened now. In the study, the Game begins. You need to solve the magnetic puzzles. When you push the cube in any direction, it moves until it runs into something. The strategy here is: don't touch the controls until you figure out how to solve it. Imagine the cube's movements. And when you know how exactly you should move it to get it to the destination, do it. Pay attention on the 7 books on the table, and number 7 written on it - it's a clue that quantity of books in every room is important. Don't forget to pick up the key from the table.
In the bedroom, read the Jigsaw Note to find out more about the story, and note the two books standing under the mirror.
Now go to the children's room. It is opposite the bedroom. Here you can see five books scattered around.
Now you know the three numbers: 7, 2, and 5. Where should they be used? Of course in the code lock to the right from the children's room. Input the code, open the door and take gears from the old broken closet.
Use gears to open the Jigsaw Box on the toy horse in the children's room. Take the key and use it to open the metal door in the basement, which is located behind the broken wall.
Congratulations, you finished all puzzles in the Abandoned Mansion. Now just go forward to get into Underground Sewer Canals.