"But in dancing, it seems I'm suppose to pickup my left foot when the music starts then wait to count one until I put that foot back down"

That's a somewhat unusual dance class if you are spending time with a foot noticeably off the floor.

Think of your foot as the stick, and the floor as the surface of a drum. Your body is an instrument in the band.

What you want to do is be, "Almost late".)

As I said, you would play your body as you would play a drum. You should be able to count the music exactly as your foot hits the floor.

Again, this is the old way.

So, in the waltz; by the time the drummer counts 3 the dancers are counting 2?

This seems unnecessarily odd to me. I wonder why it is done that way.

"So, in the waltz; by the time the drummer counts 3 the dancers are counting 2?"

I sure hope note. Anyone who wants to go anywhere with their dancing will quickly realize that the step numbers do not equal the beat numbers. If you are going to be pronouncing numeric words while dancing, those had best be the beat numbers or their fractions and not the step numbers.

If you want to be pronouncing something that matches the steps, use words that share the timing properties of the steps, such as slows and quicks and their subdivisions.

Wow ! After reading all of the resposes even I am getting light headed.

You did not mention the dance in Question but here are some rules any good dancer should know. # 1 never "pick up your foot from the floor" Even in a smooth or Standard dance where you will start off with a heel step, you should slide the insde edge of the ball forward until it becomes necessary to strike with the heel.

Assuming there is no starter step,your body weight should be received fully onto the foot on the beat. The knee should be lowering towards the floor slightly to get the weight down into the floor (on 1) As the free foot passes under the body,(brushing) You can imagine being able to reach down with both hands and pick up two buckets of water. (now you have arrived on 1 and ready to proceed.

By the way, advanced dancers will use a starter step at the very end of the previous musical phrase (the right foot)

You would be better of to count through the previous phrase and emplply the starter over the last 2 beats of the phrase. Thge starter step could also be a shifting of weight as someone else mentiond. ( you shift the lady to your Right side to prepare to move the left foot) I am assuming you are a leader by the way. (since counting is such a big deal for you)

If you are doing American or night club cha cha, the foot does move to the left side on 1. By the way , you should always double up you counting. for example Rumba has 8 distinct beats not 4.
You can count 2& 3& 4& 1(&)(step on the numbers and brush your feet on the &'s)