The best way to learn how to ballroom dance is to take private lessons.
I'd like to end my post there, but I will elaborate...
Private lessons consist of you (with or without a partner) learning dance steps and techniques from a trained professional dance instructor.
There are community education classes available in most cities. These are a great first step (hahahaha, dance pun!) to see if you like the idea of ballroom dancing. You will not learn to dance in one or even two of these sessions. Nope.
But you will learn the basic patterns associated with a few dances (foxtrot, rumba, swing, etc.) and some general direction in how to do these things correctly. Hopefully.
Most dance studios also offer group classes in various dances and levels that you can join. You will still be learning where and when to move your feet and vague corrections to make (which may or may not apply to you) while doing your "moves".
There are also many instructional dance videos. Some are great, some... not so much so. You can learn some neat patterns from these, also. But alas, not how to dance.
Unless you learn some techniques and movements that form the foundation of ballroom dancing, you will have a hard time learning how to dance from groups and videos. It will not be neat.
It will be hard to dance with other people and dancing itself might seem difficult.
Most likely, you will be doing the same pattern at the same time as your partner (so if you're single, you're out of luck), yet not actually dancing together... Like the people on Dancing With The Stars!
They do choreography. AKA- steps. Those celebs can only do what they are doing with their amazing pro dancer helping them through it and making them look good.
They have not learned how to lead and follow, use "connection," move their "centers," do the correct footwork (or why to do it), or even the basic timing for a particular dance.
Those are the things you learn in one-on-one (or one-on-two [sexy!]) lessons. You learn how to apply these fancy techniques to the basic steps and all the "moves" that come after that. You learn what is right and what is right for you (maybe you are really tall or rather petite and can't do that "perfect" frame, for example).
You will dance with someone who knows what they are doing and someone who can tell you that you drop your elbows in promenade or that you are doing the Cowboy Rumba or that your head is wonky in frame.
You will be lead or followed without knowing what patterns comes next or how it might end.
In other words, you will learn to Dance. It will be neat.