Is the fee added to the cost of the transaction or subtracted from the received money? I want to send exactly 0.00136889 bitcoin but I never sent bitcoins before, I only received.

If I send 0.0136889 to the address, will blockchain.info remove the fee from my wallet or do I need to send 0.0136889 + the fee?
The fee is paid by the sender. The sender technically specifies how much money goes into the transaction from where and how much goes out of it to where. The total output value – of course – can at most be as big as the total input value, otherwise the transaction is invalid.

When you send money using a wallet software, you specify how much money you want to send. That is, you specify how much money you want to arrive at the recipient. The wallet will then add the fee to it. Your balance will go down by the money you sent plus the fee you chose.