To make Ethereum (ETH and/or ETC) transactions with Ledger, you need:
This application is an account manager, where you can send and receive Ethereum transactions and check your balance.
The only way to open it is to connect your Nano S or Blue, make your PIN code and launch the Ethereum app on your device. Without the device, the app won't launch.
You'll then have to choose on your computer between Ethereum and Ethereum Classic. Please be careful to choose the right wallet as it would be difficult - but not impossible - to recover tokens sent on the wrong account.
For each sending transaction, your application will ask you to verify it on your device: your device will display the amount, recipient address and gas rate you will have to manually sign by confirming everything is alright on the device.
UPDATES & TROUBLES
The Ethereum application updates automatically, you don't have anything to do. Each time Ledger releases an update, it will be synced after a few hours on your computer. If you want to force an update to the latest version, just restart Chrome.
If your Ethereum app doesn't open, please consult this article.