First, you need to make sure that your firmware is updated to 1.2.
MyEtherWallet is a popular online Ethereum wallet which you can use as an alternative of the Ledger Ethereum Chrome application. It supports natively Nano S on Chrome and Opera, without the need to install any app or plug-in.
To manage your Ethereum account, go to MyEtherWallet and select the "Send Ether" tab. Plug your Nano S, select the Ethereum app and go to the settings of the app to activate "Browser support":
This will enable the direct connection to the browser and MyEtherWallet will be able to detect your device (note that if you wish to use the Ledger Ethereum Chrome application, you'll have to disable browser support).
Select the "Ledger Wallet" option and click on "Connect your Ledger Wallet"
It will show you a popup where you'll we able to select which address you want to manage:
And voilà! You can now send or receive ETH/ETC transactions.
All outgoing transactions will require a confirmation on the Nano S (exactly like with the Ledger Ethereum Chrome application). Only public data is sent to MyEtherWallet and your private keys will never be exposed to the browser.
Once you confirm the transaction on the device, please wait a few seconds for the signature to complete. It'll then show the raw date on the web page, and you must click on "Send transaction" again to display the final confirmation popup:
A tutorial to securely manage your tokens (REP etc) is available here.