How do I use my Tax-Exempt number to avoid sales tax on my purchase?
You don't need to.
Orders shipped to addresses outside of California are not charged sales tax, so there's no need for you to give us your tax-exempt number. Of course, depending on the laws of your state, you may be required to pay "Use Tax" on purchases made from out-of-state. This is true in most states with a sales tax.
Orders shipped to an address in California are subject to applicable sales taxes.
It might be a surprise to everyone except California teachers, but schools here in California have to pay sales taxes just like everyone else. (No, it doesn't make sense to us, either, but there it is...)