Timestamps are displayed if the current message is more than 15 minutes newer than the previous message. To immediately see the timestamp on a message, you can simply tap the message.
You can also tell the app to automatically show all timestamps by enabling "Timestamp Every Message" in Settings > Theme.
For old messages, timestamps display the date and time, whereas for recent messages, the day and time, or even just the time, is shown. If you want to see the exact date and time a recent message was sent/received, long-press it, then tap "More" and select "View Details".