Keep in mind that it is only possible to message customers (not other writers) and only if they have an order in auction or an order with you.
If an order is in auction, you can message the customer after you place a bid.
Such chats are available as long as an order is in auction. If the client hires you, you can continue chatting. If they hire another writer, the chat in that order will not be available for you anymore.
If you were hired for an order and want to message your customer, just select the order you need on the "My Orders" page and send a message in the chat.
Keep in mind that order chats are active only for 30 days after an order is completed. So, if an order was completed more than a month ago, you cannot contact that customer unless they place a new order.