Not bad. There is no "long random number" that is a "money number", you might want to research a bit more how transactions work.
Essentially, if someone wants to send 3 bitcoins (300,000,000 Satoshi) to someone else:
The sender creates a message that lists which of the prior unspent transactions they've received that provide a total of at least 300,000,000 satoshi of value. These are "inputs" to the transaction.
Then the sender adds to the message the address (actually a hash of the public key) that is receiving the value from the transaction. The sender then adds in indication of how much of the value that is being used should be associated with the new address. The combination of address and value is an "output".
Finally the sender provides digital signatures to prove that they have the authorization to spend the "inputs".