Typically at closing is when you would put down your down payment, but it will depend on a few other things. However, if you are building, your builder might require you to put a certain percentage down prior to breaking ground as your earnest money deposit. If you are purchasing a previously owned home your earnest money deposit may only be 1% of the purchase price.
This is a great question for your Buyer's Agent who you want to have representing your interests. If you've already selected one, they should be able to get clarification for you promptly.