If you want to send a quote via email, go first into the quote's detailed view via Quote in the menuand click on the customer. In the action bar at the bottom of the page, select Email as Action and then Send.
Note that you must have a recipient address specified on the customer in the customer registry under Document Delivery Options in order to be able to send a quote via email.
You must also have a sender address registered under Settings - Sales Order/Invoicing/Purchase Order - Email Documents.
An email with the quote as an attachment is sent to the customer. In the list, there is a symbol indicating that the quote was sent by email. If you hold the cursor over the icon you see when the mailing occurred as well as to which recipient.