How do I see an image comment added on a Nikon camera once I download a picture?

The comment is really saved, but it's in the photo file's metadata — a collection of information in each file describing the photo, the camera it was taken with, the camera settings, and so on.

In the manual (page 138, Nikon says that you can see this with the included ViewNX 2 software. That's true, but you can also see it with any photo viewer which includes metadata support.

There are several different metadata standards, and here Nikon uses the most widespread, called "EXIF", and they use the UserComment field from that standard. (For the very technically-curious, it's tag # 0x9286.)

I'm not sure what operating system you are using, but the simple command line tool jhead will work on Mac, Windows, or Linux. Download it and run

jhead dsc_1418.jpg 

(or whatever your actual filename is, of course), and you will see output like:

Camera make  : NIKON CORPORATION
Camera model : NIKON D5100
Date/Time    : 2013:04:18 09:15:31
Resolution   : 3264 x 4928
Flash used   : Yes (auto, return light detected)
Focal length : 112.0mm  (35mm equivalent: 168mm)
Exposure time: 0.033 s  (1/30)
Aperture     : f/5.3
ISO equiv.   : 800
Whitebalance : Auto
Metering Mode: pattern
Comment      : Here is your Image Comment!

It's likely that any software that advertises itself as an image viewer will be able to handle this.

Open the digicam's Setup menu and select Wi-Fi. Select Network Connection after which select Enable. Select Network Settings to display the screen shown on the proper. Select a connection option. Launch the Nikon Wireless Mobile Utility app for your tool.