Your very best friend, when it comes to cleaning your Xbox One, is a dust cloth. That's because as long as you keep the exterior clean and dust free, you shouldn't ever have to clean out the inside of your console. A dust cloth lets you grab most of the dust that can accumulate on your system.
All you need to do is run the dust cloth over the outside of your system. This includes the top, bottom, sides, and ports. Depending on how long it's been since you've wiped down your Xbox One you may need to clean off the cloth a few times, but for the most part this method will get the job done.
If it's been a while since you've cleaned out your Xbox One, then you might notice that there is dust everywhere. On the top and sides of your console, as well as in all of the grates. While a dust cloth can easily deal with everything on the outside of your console, if you've got dust inside your grates you'll need to go a slightly different route.
Thankfully it isn't hard to go ahead and clean out the dust inside those grates. All you'll need is a can of compressed air. Using the detail nozzle, use short directed sprays to clean the dust out. This should only take a few minutes, and you'll be able to see when the dust has evacuated the area. Canned air is also useful for getting into all of the ports along the back of the Xbox One. These can easily collect dust, but they're hard to get into with a cloth (and you'll probably end up leaving behind lint or shreds of paper towel if you do).
Of course, in doing this you'll be kicking a bunch of dust into the air, and inevitably that's going to settle back on your Xbox. So give it a few minutes and then come back with the dusting cloth and give it a quick wipe down.
Avoid damp wipes
Now plenty of folks use wipes doused in cleaning chemicals (or even a bit of water) to clean just about every surface in their homes, from countertops to windows to TV screens. Most of that's fine. Do not use them on your Xbox One. Specifically this is because your Xbox One is covered in vents, and you don't want moisture of any kind to seep in there. Really, you shouldn't use these on any electronics — TV and Xbox included.
In general, you should avoid using anything that is wet since it has the capacity to screw up your console. Liquid + electrical components = bad time. By sticking with the combo of a dust cloth, and compressed air you should be able to easily clean out your Xbox without accidentally causing any damage to it.