When a business is fully booked you can ask to go on their waitlist. If somebody cancels, they can offer the slot to you.

Why it is worth doing
Cancellations happen constantly, often at short notice. Being on the list is the difference between hearing about them and not.
What to tell them
Which days and times actually work for you. A waitlist entry saying anytime is less useful than one saying weekday evenings, because they can match you to what comes up.
Being quick
Slots that free up tend to be close at hand, so an answer within the hour usually gets it and an answer tomorrow usually does not.
Classes
Group sessions often have a waitlist too. Popular classes rely on them, since somebody nearly always drops out.
Common questions
How will they contact me?
However you normally hear from them, which is usually email or text. Keep your details current.
Does joining a waitlist cost anything?
No. It is a note that you would like a slot.
Can I be on more than one waitlist?
Yes, with as many businesses as you like.