Apart from accenting the offbeat, the most important aspect of a dance rhythm when actually played is that the instrument produce a weaker sound on the offbeat, and a stronger sound on the main beat -- to dovetail naturally with the rhythmic weakness vs. strength, as well as the weakness vs. strength of the bodily motion that the dancer is making on the offbeat vs. main beat.
Weak rhythmic beat, and a weak wind-up motion in the dancer -- weak sound from the instrument. Strong rhythmic beat, and a full delivery-of-force motion in the dancer -- strong sound from the instrument. Again, "weak" sound does not mean silence. There has to be some sound, just not as attention-getting as the sound of the main beat.
The primary set of instruments for creating the rhythm is percussion. The main beats, especially in a dance song, will be made by the bass drum -- a strong, booming, low-pitched sound. The "backbeat," or the relatively weaker main beats of 2 and 4 (compared to the more prominent 1 and 3), will get a snare drum -- still pretty forceful and noticeable, but higher pitched and not as booming. Then for the offbeat, that leaves the cymbals, usually but not always the hi-hat in a standard drum kit. They're quieter, less resonant, and higher-pitched than the other instruments the drummer plays.
Secondary rhythmic instruments follow the same principles. For a guitar being strummed rhythmically, rather than to carry out the melody, there are two motions made, just as with a dancer -- a weaker upward strum and a stronger downward strum. Offbeats require an upstrum, main beats a downstrum. When the rhythm guitar is used to accent the offbeat -- that is, to play only those offbeats, making them really stand out by not mixing them in by playing the main beats -- you get the characteristic choppy "skank" guitar rhythm of ska music, which is what makes it so danceable.
(I'll do a separate brief post on ska's 15-year cycle, in which the style emerges during the restless warm-up phase of the excitement cycle, as part of the broader dance fever of that phase: the early '60s, late '70s, and early '90s -- albeit with an absence during the late 2000s, with a potential revival in the early 2020s to be determined.)
The brass instruments can be played only on the offbeat, such as in ska. Weaker sound on the offbeat means a lighter puff of air, rather than a blaring lung-emptying honk.
Keyboard instruments can be played rhythmically -- early R&B music could use a single piano chord to play both the offbeat and main beat, instead of the drummer hitting those beats on the cymbals. The weaker sound on the offbeat comes from simply applying less force to the pressure-sensitive keys.
And as new wave and synth-pop developed, they used the synthesizer to play notes or chords rhythmically rather than, or in addition to, playing them melodically. Their keys are not necessarily pressure-sensitive, so they instead varied the pitch -- high pitch for the offbeat, low pitch for the main beat. To make it clear that these were supposed to be perceived as a pair (with a weaker twin and a stronger twin), they played the same letter-note (say, C) in two different octaves. This "octave bass synth" produces a very bouncy rhythm, perfect for alternating the dancer's body between its wind-up and delivery motions.
Finally we return to where we began -- the human voice. Not singing the lyrics, which is part of the melody, but human speech sounds used to accent the rhythm. Calls, filler words like "oh!", and the like. Weaker sound for the offbeat usually means less phonetic stress.
But while just about any instrument, or voice, can be used rhythmically, the percussion instruments form the backbone, so we'll focus just on them to get the basic idea.
From a recent post on the return of the disco-punk style, here's a brief explanation of the disco drum pattern, which is the template for all modern dance music. Remember there are four main beats per measure, with four weaker offbeats in between: "1 and 2 and 3 and 4 and..."
Typically a dance rhythm will use the hi-hat cymbals on these "and" offbeats -- and usually, only the offbeats, not also the 4 main beats. For a standard disco beat, there is a bass drum on all four main beats (and none of the offbeats), and a snare drum on the 2 and 4 beats (and none of the offbeats). Listen to this brief explanatory video. The disco beat is just one example of a dance rhythm that uses little sounds on the offbeats, which is the most important aspect for our purposes -- whether it has a bass drum on all four main beats is not.
For examples, see the post linked to above, which has several linked and embedded videos.
The next and final post in this series will do a quick historical survey of when these simple-step dance rhythms explode in popularity, and how it relates to the social and emotional changes taking place during the restless warm-up phase of the cultural excitement cycle.