It depends on what level of Cubase you have. Cubase Pro calls them cue channels. I see you are looking at Cubase LE/AI.
First, you need hardware – some sort of audio interface or sound card for the headphones to plug in to. Then it needs a driver (which is generally written by the hardware maker). (A driver is software that interprets the operating system for the hardware and vice versa.) Therefore, the operating system can make the hardware available to apps like Cubase. Under menu item “Devices > Device Setup” there’s “VST audio system”. This is where you connect to the driver. There’s ASIO4ALL, which is a generic fallback driver, which you should only use if you have to. There’s a sub item under VST audio system that’s driver specific. Going in there, you can see what’s active. looks like this and this.
Now under Devices > VST Connections there should be a tab for output, which will have a bus for stereo out, and that should be connected to your audio device (= hardware) and output ports, which will be named as they were named under VST audio system. Looks like this
You probably have all this set up correctly if you are hearing any sound out of Cubase. If your hardware has only one output for headphones, then you wouldn’t be asking this question, so there are at least 2 stereo outputs. All you need do at this screen is to add an output bus. Give it a name like “cue mix” and assign the device ports for that second stereo output. The manual is pretty lucid about the details, but there are some important issues that need attention.
First, what’s your latency? Chances are that it will be too much, even if you have great hardware. Even 5ms is distracting for the singer, who may hear a digital delay effect. You are going to want to use ASIO direct monitoring to get around that issue, which basically means sending the mic input in 2 directions out of the hardware device. One signal copy goes on to Cubase for recording, the other makes an immediate U-turn to the singer’s headphones. How to do this depends on your hardware. If you can do it in the hardware driver or utility software, or by some kind of button on your interface, then that’s probably your best bet. Since I use this option, I have nothing to say about the alternatives, but there is a direct monitoring checkbox in the hardware specific sub-item of VST audio connections, which hopefully isn’t greyed out. In the worst case, you may just have to live with it. Try to reduce the latency by reducing the sample size your hardware is using. Reducing the sample size increases the risk of drop outs, so you’d have to experiment.
The other important issue is how to route the rest of the cue mix to the singer’s headphones. Using the main mix is an option, but that normally allows the singer to hide behind the band. Preventable mistakes are made, but not noticed, until the mixdown, or until the vocal is played back in solo. So you want to deliver a thin mix to the singer (for example: quiet drums, and one quiet instrument with pitch). This will involve going to the mix console and using sends from those channels you want the singer to hear to the output bus called “cue mix” (or whatever you called it).