Remember that essentially a pen display is a plastic box that contains two separate devices: (1) a pen tablet and (2) a display.
We need to account for 4 things to use a pen display.
Power to tablet
tablet component
very little power is needed
Data
tablet component
for example, pen position data is sent to the computer. Also the computer can send data to the tablet such as a firmware update
Power to display
display component
much more power needed than the tablet component
Display signal
display component
What is shown by the tablet
This document is going to talk about connectors a lot. So you need to know what they look like first. Read this guide on different display connector types before you continue.
Those four components are distributed over cabling differently, depending on the the cabling option involved.
Some pen displays can run on a single USB-C cable. This used to be uncommon. But Increasingly many pen displays support this option. More here: Connecting a pen display with one USB-C cable
One USB cable for pen tablet (power, data)
One power cable for the display power
One display cable to carry the display signal - This will almost always be an HDMI cable. Though some tablets support alternate connector types for the display signal
one cable provides power for the display component
one USB-C cable handles everything the other 4 components
The 2 cable setup is how I use my Wacom Cintiq Pro 27.
This is a special kind of cable. One end will have a single USB-C connection. The other end it will have the different connections. Typically these will be: HDMI, USB-A, and some kind of power. More here: 3-in-1 cables
HDMI connectors are extensively used. So let's start by addressing HDMI which shows up in option B and option D.
In principle this is easy: Take the HDMI from the pen display and find an HDMI port and plug it in.
For the vast majority of you this will "just work".
But now let us explore all the complications
If your computer has multiple HDMI ports you need to pick one.
If it's a laptop - it shouldn't matter. Any HDMI port should work.
If it's a small form factor PC - then also it shouldn't matter. Any HDMI port should work.
If it's a PC that has a separate graphics card you might have an HDMI port in multiple very different locations
You could have HDMI ports on the graphics card
You could have HDMI ports on the motherboard of the computer
As a general rule, always use the HDMI ports on the graphics card
Only use the HDMI ports on the motherboard as a last resort.
Sometimes you'll read a statement like "HDMI doesn't work on the motherboard". That's kind of an exaggeration but its a well intentioned one. But it is true that sometimes HDMI ports don't work on the motherboard. Let's go through the reasons.
First, to get an motherboard HDMI port working you need several things to be true
First the HDMI port must exist
Second, the computer has to have a component that sends a display signal to the port. This is called integrated graphics. It's called "integrated" because the graphics component is on the CPU.
Third, the use of the HDMI port must be enabled.
What often happens is, not all these conditions are met with motherboard HDMI ports on all PCs.
The HDMI port might exist, but there is no "integrated graphics" - so that port won't work
You might have the port and integrated graphics is available, but also the BIOS might be set to disable the use of that port. So you'll have to enable it in the BIOS.
Finally, some computers have an interesting behavior where, if a graphics card is installed, then they automatically disable the motherboard HDMI. In other words, you can either use the motherboard HDMI or the graphics card, but not both.
You aren't going to hurt your computer by trying to use motherboard HDMI, but you should know why it might not work.
These will work, but there is one thing you should be aware of. Sometimes graphics cards have N ports, but only N-1 can be used simultaneously. I have a card like this.
If you have two ports that work - one on the motherboard and one on the graphics card, then which should you pick? The answer is ALWAYS try the graphics card HDMI first and only use the motherboard HDMI as a last resort.
First, Motherboard HDMI support just isn't as powerful as what you will typically find on a graphics card from the same era. The motherboard HDMI may not support 4K or may not support a high enough refresh rate. So it might, work but your experience might be degraded.
Second, both motherboard HDMI and the graphics card need to use memory to do their work. A graphics card comes with its own memory that is dedicated to dealing with graphics. Motherboard HDMI as far as I know - does not use any dedicated memory - but instead uses the same memory as the CPU. This means that you CPU is "losing" some memory so that the motherboard HDMI can use it instead.
If you need to make an HDMI connection but have no HDMI ports you can convert other ports to HDMI using an adapter. See Using HDMI adapters with pen displays
When you've connected your display you might see it show a message saying NO SIGNAL. Here is a troubleshooting guide to work through the NO SIGNAL problem.
Go here: Connecting a pen display to a mobile device
No pen displays connect wirelessly. They all require at least one cable to connect to your computer.