At its simplest, a de-esser is just a compressor.  More specifically, a de-esser is a compressor which often implements a dynamic threshold, a high-ratio reduction curve, and a high-pass filter in the sidechain.

A dynamic threshold is important to a de-esser so that the compressor limits vocal fricatives (or sibilance) relative to the overall loudness of the material.  As the loudness of the entire input signal goes up, so does the threshold.  Otherwise, the sibilant sounds would be capped at a specific loudness, which would sound very unnatural contrasted against the fluctuating 'voiced' portion of a vocal.

The Massey De:Esser uses such a dynamic threshold.  And, the reduction control determines how much gain to apply to the sidechain control signal, to push it over that threshold.  (The markings on the reduction slider are simply reference points, and do not indicate dB reduction.)

The frequency control determines the cut-off for the internal high-frequency filter, which then forms the compressor's sidechain signal.

When the band-split option is enabled, the plug-in splits the audio input into a low-frequency portion and high-frequency portion (using a linear phase filter.)  This allows the plugin to affect the high-frequency portion of the signal, and leaves the lower frequencies less affected.  The frequency cutoff point is defined by the frequency knob.

For vocals I recommend leaving band-splitting off. I find that single-band de-essing sounds most transparent even though this might at first seem counterintuitive. The reason, I believe, is that sibilant and voiced sounds, in English at least, rarely overlap much. There's usually a pretty sharp demarcation in the time-domain, so a simple gain reduction has the required precision to neatly chop out the extra sibilance. Band-splitting is always going to have a transition frequency-band between the sibilant and voiced signals. This transition band, though quite narrow in this plugin, still ends up muddling vocals unnecessarily.

The dry-wet (a.k.a. ratio) control lets you blend the input signal (dry) back into the affected and compressed output (wet) signal.  It's useful to note that applying a wet/dry mix to a compressor simply results in a reshaping of the compression curve.   Effectively, you are reducing the compression ratio as you blend back to the dry signal.  You can think of the dry signal as passing through a compressor with a 1:1 ratio (no compression.)  Mixing the two signals then gives you a ratio in-between.  You will notice that this nature is reflected directly on the reduction meter -- as you decrease the dry-wet control setting, the amount of metered reduction will also decrease.

The Massey De:Esser has two listen modes that can help you find the most optimal settings.  The default listen mode is called invert (indicated by the null symbol). The second is called filtered (indicated by the high-pass curve icon).  The filtered mode is pretty typical for a de-esser plugin and lets you hear the high-pass filtered signal that is feeding the internal sidechain portion of the algorithm.  

In invert listen mode, the plugin subtracts the input signal from the normal output.  This results in an output signal that is very quiet when the compressor isn't operating, but lets through the de-esser's result when it is compressing.

I find invert mode to be much more useful.   It really lets you isolate what the plugin is doing and when.   It becomes very obvious when the de-esser is digging too far into the voiced portion of a vocal, indicating that you need to increase the frequency setting (or decrease the reduction control.)

The top-most button in the listen section determines when the listen mode is enabled.  When auto is indicated, listen mode is enabled whenever the frequency control is touched.  When on is shown, listen mode is constantly enabled. Off disables listen mode altogether. (Note: auto mode is incompatible with a control surface and only functions when operated by mouse.)

If you click the very bottom of the plug-in's user interface, four additional controls will be revealed:

The response control changes the behavior of the dynamic threshold.  There are three modes with the cryptic labels X, V, and D.  On vocal material, V and X are probably the most useful, with X being more aggressive than V.  D responds more slowly and was designed to sound better on drums.

The speed control alters the reaction time of the de-esser.  Moving the slider to the left (towards +6) increases the speed.  Moving it to the right (towards -7) slows the action of the de-esser.

The re-ess option inverts the operation of the de-esser and actually accentuates any sibilance.  What for?  I don't know.  I'm sure you'll find a use for it (probably on something besides vocals.) The dry-wet control is inactive when re-essing is turned on.

Last, the output trim should be pretty self-explanatory.  It lets you change output levels of the de-esser.  The re-ess option inherently brings down the signal about 12 dB.  So, the output trim might be useful in that situation.