Handsets with the Google Experience Launcher, like the Moto X, allow you to launch Google Now by simply saying "OK Google." To add this functionality to most Android phones, you'd have to install the Google Launcher, which would override the launcher currently in use (even custom ones).
With the Samsung Galaxy Note 3, you don't have to override your current launcher to get convenient access to Google Now; the always listening feature is built-in, it's just pointed to the wrong app (S Voice). By using one app, S for Switch Voice, you can use the default Note 3 voice command, or the Home button, to launch Google Now. Here's how:
Note: This shortcut application is not perfect. You will likely still see the S Voice app for a second before you are forwarded to the Google Now app. However, it does offer a convenient way to wake the phone up to the assistant you want to use, instead of to the app Samsung has designated for you.
Before installing the app, open S Voice by pressing the Home button twice, then press the menu button. You will see a switch next to "Voice wake-up" -- make sure this is enabled.
As an option, if you also want Google Now to launch when pressing the Home button twice, make sure there is a checkmark next to "Open via the home key."
Now you're ready to install S for Switch Voice on your Note 3. After the install, tap on the app's icon to open it. You will see an alert asking to install a Secure Settings plugin, press No. You do NOT need to install this plug-in, it is primarily for rooted users.
Reboot your device. Now whenever you say "Hi Galaxy" your Note 3 will wake up and Google Now will be waiting for your first instructions. If you want to give Google Now another command, use the default "OK Google" voice cue. One caveat: If you have a security setting such as a PIN or pattern, you will have to complete that before the device can load Google Now.
Now that you've ditched S Voice, learn the secrets of of Google Now voice commands to maximize its usefulness.
If you want to replace the double-press Home button shortcut on Android with an app of your choosing besides Google Now, check out Sharon Vaknin's guide to on how to customize Android's Home button shortcut.