To make an order tax-exempt, you must first set the customer to tax exempt.
Go to tools / customers and search for the customer you want to be tax-exempt.
Click edit customer info in the upper right of the page.
Check the tax exempt box and save (see image below)
Now you should be able to place an order for the customer without paying sales tax.
Another way is to temporarily edit a product to be tax exempt and then switch it back after you place the order.