The Messages app in does not display timestamps for each individual text message or iMessage. It simply provides a timestamp at the beginning of each new conversation. If you ever need to go back and see when a particular message was sent or received, there is a simple way to see the timestamp of a message.
View a Timestamp
While in the Messages app, tap on a contact from the list to open the conversation list for that person. Once you open a conversation list, you will notice the timestamps at the beginning of each conversation are displayed.
Drag your finger from right to left anywhere within the message area. The messages will slide left and the timestamps for each individual message will be revealed.
When you are finished viewing the timestamps, release your finger and the messages will slide back to their original location with the timestamps hidden.
The Copy and More… Options
When trying to drag your finger from right to left, you may notice a bubble with the Copy and More options will appear above a message. This will happen if you hold your finger on a message for a second or two. Tap anywhere in the window to make the bubble disappear.
Not wanting to completely ignore these options, they are worth a quick explanation as you may find them useful.
This option is pretty straightforward. Selecting Copy will copy the contents of the message that can then be pasted into another message or app.
When you select this option, the window changes to what you see below.
From this window, you can select individual messages by tapping the circles at the left. A check mark will appear when the message is selected. The selected items can then be deleted by tapping the trash can icon or forwarded to someone in a new message by tapping the right facing arrow at the bottom of the window. Tapping Delete All in the top left of the window will delete all the messages in the conversation.
If you have additional questions about the Messages app, please see my other articles about text messages and iMessages.