There are 2 ways of marking a customer as tax exempt.  The easiest way to make a customer tax exempt is at the time they place an order.

At the time of ordering:

When customer places an order, add them to the order then check the 'Tax Exempt' checkbox on the top right and enter in their Tax Exempt ID number.  Note you can enter in any placeholder number here if they don't have it readily available.

The next time the customer places an order, the system will remember they are tax exempt.

On the Customer's profile:

If you want to make a customer tax exempt without them placing an order, go to Orders >Customers >search for customer and select the one you want.

Click Customer Account Information > scroll down and turn Tax Exempt Status to Yes and then enter their Tax Exempt ID number. Be sure to click Save Customer!  When this customer is added to an order, the system will remember they are tax exempt.