How do I find out the miners fee for my transaction using Blockchain.info API?
There really isn't a standard fee value. Various clients implement different amounts. For example on my MultiBit installation it's currently set to 0.0001 BTC per 1000 bytes of transaction size.

You must include a fee otherwise miners won't confirm your transaction.

For Blockchain.info's case, using their API, if you don't have the $fee parameter, Blockchain.info will automatically add 0.0005 BTC in fee, which is the default value.


  All transactions include a 0.0005 BTC miners fee.


So if you send 0.01 BTC with their API, and don't specify the $fee parameter, it will add a 0.0005 fee to your transaction. 

EDIT This means you actually need at least 0.0105 BTC (0.01 + 0.0005) in your wallet to make the transaction. If you want to send all of the 0.01 BTC, you have to actually send 0.0095, otherwise the transaction won't go through.