Will the miners mine my new currency by using the same miner as Ethereum? And will they need to configure their miner to specially mine my currency? I would be grateful if someone can explain me how this works for me, now I have created my new currency under the Ethereum technology.
The miners will mine on the Ethereum Blockchain, they do not need to mine your currency specifically: they secure all contracts on the chain.
Just to elaborate a little on Olmo's answer, your token is a Smart Contract. The entire Ethereum network works together to ensure Smart Contract code executes as written.
Your token is riding "for free" with the rest of the tokens out there. (Not really for free, because you'll still be paying out transaction fees to miners for executing your token smart contract.)
If you'd like to give miners an extra reward, it's not outside the realm of possibility. You could always include transferring some of your token to
block.coinbase. (Found on: http://solidity.readthedocs.io/en/latest/units-and-global-variables.html#block-and-transaction-properties) I've never seen this done yet, just an interesting thought experiment. You could only transfer when your contract is executed. Miners wouldn't know they have your token unless its popular or you tell them about it.
To answer your question directly, your token is secured as much as the rest of the Ethereum Blockchain.