Use the “+” icon in the top-right corner of the DM screen to start a new conversation. Quickly pick from the auto-generated list of people you follow, or search for someone new. Add one person, or multiple people, then click the icon in the top right corner to send a message.
Use the "Type a message..." input box to send something. Messages will be displayed oldest to newest. Your messages will appear on the right side of the screen. Anyone else in the conversation will appear on the left side of the screen.
Control DM push notifications from the Settings=>Notifications screen. Don't want to miss a message? Toggle the "New Messages" notification ON to receive mobile push notifications.