One of the most challenging things for most people when they start to get serious about dancing is finding the beat. In competition, if a couple is off time they are placed last no matter how good the technique or showmanship.
All music starts at the beginning, and the beginning is always a "1" beat. Although some songs have an intro that may use a sound effect or snippet of conversation or other unconventional treatment, the first true musical beat you'll hear in the song is usually a "1" beat. Learn to hear this and things get much easier.
Dance music has timing aspects that make each dance unique. The swaying 3/4 time of Waltz is dramatically different from the crisp 2/4 time of Samba, for example. One bar in Waltz will go from the "1" beat to the "3" and then start again, while one bar in Samba will only include the "1" and "2" (though in Samba and other dances there are actually 8 beats in total, which is why things are grouped into 8 parts). Dances that rely on 4/4 timing will use a bar that goes from "1" through "4."
Throughout the song, the "1" beat usually receives slightly more emphasis. That doesn't mean it's louder. In fact, it may even be quieter than other beats. But it's deeper and feels like a down beat. It somehow has more presence and you'll have to learn to pick it up. There are some songs where it even feels like a hole in the music, making it easy to notice. Once you learn to hear the "1" you'll start to see the bars of music unfold without even thinking about it.
The only way to get there is to listen to lots of music. Even listening for the beat count in non-dance music will help. After a while you'll find it quite easy to "feel" where the "1" beat is and you won't have to rely on hearing that first note to pick it up.
Strict tempo music is easier for this purpose because it makes an effort to define the "1" more clearly, while chart hits (which are written for artistic style, not dancing) will sometimes be quite uneven in their emphasis. Many chart hits even put the emphasis on the "2" which creates unique challenges for the dancer, because the music is king. In such cases, experienced dancers will change their starting point to let the music flow better with the dance. But for most purposes, International style ballroom dancing always orients itself to count from the "1" beat.
Latin dances have unique challenges related to the beat.
In Rumba there is a visible "holding" of the beat from the 4 to the 1. So you have "2, 3, 4 (hold)." During the hold the body continues to move as weight shifts but the feet don't move.
In Cha Cha Cha there is a split beat on the 4 where the feet do a Sashay step, three quick steps often called the "cha cha cha." So you have "2, 3, 4and1" or "2, 3, cha cha cha."
It would be nice for novice dancers if all dance music clearly defined those points. For example, if all Cha Cha music only split the beat exactly where the Sashay is supposed to take place. Unfortunately, not all dance music makes it easy, but that's actually a good thing. If all the music for Cha Cha had a pronounced split beat exactly where you want it, the audience would find the dance boring to watch because it would be too predictable. There is a balance between the movements and the music that creates beauty. Experienced dancers will even play with the music, putting extra motion where the song has less emphasis to keep the dance interesting. This is called "syncopation." At higher levels of dancing there are also special timings that hold the action through one or more beats for powerful emphasis.
For this reason, you'll hear split beats throughout a Cha Cha tune, even where dancers aren't supposed to have extra steps. Some songs will even seem to be more subtle on the "4and1" rather than clearly splitting the beat there.
Never train yourself to hear the "ChaChaCha" Sashay in Cha Cha music. Instead, train to hear the "1" in all music and you'll automatically know where to split the beat (or hold the beat) because you'll know where the count begins.
The Samba and Jive add additional challenges. To beginners, both of these dances sound very much like "1and2and3and4." In actual fact, they have deeper complexities you learn to appreciate as you get more experienced.
Proper Samba music is actually made up of 8 beats. Listen carefully and you'll discover that a typical verse in Samba takes exactly 8 beats from start to finish. The first 4 go up slightly, the second 4 usually go down. This is important and the reason why everything in Samba is done to the count of 4. In Samba, there are 5 different kinds of tempo, some using half a beat, some a quarter, some three quarters and some a full beat. When you change from one tempo "type" to another, you want to do so at the end of a 4 count or an 8 count so that your sudden change of motion ties directly into the music.
Let's say you're doing Voltas then Bota Fogos. 4 of each adds up to 8. If you start at the beginning of a verse, you finish your Bota Fogos at the end of the verse, which becomes very attractive because you then make your next change where the music changes. Now if you do an extra Volta, you'll be putting yourself in an awkward position because then your Bota Fogos end one bar into the next verse of music. Do you see the problem? That's why Samba has such carefully defined groups. If you make a mistake and do 5 instead of 4, compensate on the next group to bring you back in line with the music.
Jive isn't quite as challenging, but it has its own unique pattern. While there are technically 4 beats to a bar of music, there are really 8 beats to a phrase, and this can be used very successfully once you get more sophisticated as a dancer. If you listen closely to Jive music, you'll discover that there's a very distinctive "down" beat followed by a distinctive "up" sound in every bar. Your dance will look slightly wrong if you begin your rock steps on the "up" beat because your body will be moving down while the music will be subtly moving up. Learn to feel the difference and you'll dramatically improve your Jive.
Standard dances also offer surprises, even to experienced dancers. Many dancers are quite shocked when they learn that the Viennese Waltz actually has 8 bars to a phrase. That's because they are first taught to recognize only the individual 123, 123 beat count and stick with this for years. The best way to count Viennese Waltz is not the usual 123, 123 beat count but a 1... 2... 3... bar count, allowing an entire bar to encompass each count. This takes a bit of getting used to, but slows down the entire effort making it look like you have more time than people frantically counting the rapid beats. Most songs begin with 8 bars but some begin with 4 before the first full phrase starts. When you do a foot change, it always looks smoother and more natural if it is done on the 7th bar so that you can begin with either a natural or reverse turn on the start of the next phrase. The Quickstep also benefits considerably if you learn to count the bars rather than the beats.