You have to divide this question into two parts. Your confusion arises from the fact that there is no account per person like a bankaccount.
1 - If there is no account where does the knowledge of who owns how many bitcoin comes from?
The blockchain contains of information about amounts of bitcoins that have been sent to addresses. So, it knows how many ...
How is the monetary aspect of a bitcoin stored?
There is no such thing as a Bitcoin in normal Bitcoin usage. Bitcoin is a currency but it does not have the equivalent of a physical coin that passes around. Bitcoin is really a unit of measure not a coin or anything much like a coin.
Where the monetary aspect is stored depends on where you look.
Within the Bitcoin protocol, each Bitcoin is represented as 100000000 satoshis. Therefore, you can divide bitcoin up with a precision of 0.00000001.
In a transaction, the number of satoshis being delivered to each output is recorded, along with a record of which previous output is being spent.
The fee is then derived from sum(Inputs) - sum(Outputs). The ...