The phrase go down has many uses where go is a shortened form of an expression to replace several different verbs, but the action always involves movement and down can be used metaphorically to show direction
In your example
It all goes down in her notebook.
means things are written down in a notebook
Let me grab a pen so I can make a note and write that down
usually the writing surface is below the person writing
It means to travel south
We are going down to the Caribbean to catch some sun.
I'll be going down to London from Edinburgh next week.
It means to descend
Go down to the basement, the wine cellar is on the right
We'll go down the mountain before it gets dark (skiing)
It means to drink or eat
This cold beer really goes down nicely after a long day
That Muscadet goes down well with seafood
The greasy sausages went down easily
It means to travel further
Just go down the road and you'll see their house
If you go down this path you'll see the tree
It means to be noted
Rudolf the red nose reindeer, you'll go down in history
It is a type of sex
She likes it when he goes down on her
It can also mean how something is received
The play is going down well, the critics like it
The joke went down like a lead balloon
Go down is very useful indeed.
Go down may or may not be the opposite of come down
When you go down from the top of the mountain, the people in the valley will see you coming down
come down can also mean a dampening of spirits
Turning on the lights during the dance was a real come down
Running out of beer was a real come down at the party last night
For directions go down and come up are opposites
Go down to the first floor, then come (back) up to the fourth floor
Come up can also mean to appear quickly
His illness came up all of a sudden