The levitation spell is, "exani hur "up/down". The cooldown is 2 seconds, it's for all premium vocations to purchase for 500 gps at level 12, and each time you use the levitation support instant spell it costs you 50 mana.
There's plenty of places you can and can't levitate to in Tibia. Please see the direct pictures below for an example. In my pictures, the yellow checkmark means you can levitate here and the red x means you can't. You can only levitate one floor up or down at a time, not multiple floor levels. Surely you can cast this spell after the cooldown again if you need to go up multiple floor levels. You need to make sure there are no obstacles in your way, like a plant or something your character can't stand on. Some places look like they can be easily levitated on but it depends on their surface or intention. Sometimes you need to be in the right place and be sure your standing close to the place you want to levitate on. If your having trouble levitating be sure to move around to see if it's possible as certain angles won't work. When you levitate on stairs it prevents you from doing so, you might as well just walk up or down.
This spell is useful when you need to stay away from danger. Either your hiding from someone or a creature it helps you avoid conflict from above or below. Maybe you want to find a safe quiet place that no one else will go. I'd recommend having this spell on hotkey or action. Some places require you to either carry parcels or boxes with you (if you stack 3 of these you dont need levitate but people might steal them) it's best to learn how to levitate early in-game so you can safely explore. Just mess around with the levitation spell if you're having trouble. You surely will get the hang of it and maybe discover something that is new.
Places you can levitate:
Places you can't levitate: