There are several drills for both Ballroom and Latin dance. I don't think I can adequately describe them, it would be best if you had your teacher show them to you.
In general, for Ballroom, I suggest you just walk back and forth across the floor, focusing on moving your feet correctly. As you have been taught by your teacher. And do the basic steps focusing your attention on the technique you've been taught.
For Latin, pretty much the same. Do the basics focusing on your cuban motion or the technique that you have been taught.
You can practice all the steps that you have been taught without a partner. It's not the most ideal, but it's better than nothing.