How do I view text message details on iPhone?

What details do you want? The date of receipt of the message should always be visible in the main list of messages. If you go into a conversation you will also see the time of day.

The extent of other detail available will depend on a sender being in your Contacts app.

Touch on a message.

If a message or SMS is from a sender not in your Contacts app you will see at the top of the screen a 'head and shoulders' icon. Below this will be the service number sending you the message - where this has been made available by the sender. Touching on the head and shoulders will show the number again with the option to call and another icon called Info. The Info button will show nothing more than the phone number.

If a message or SMS is from a person who is in your Contacts app you will see a name of the person (if they have made their phone number available). If you touch on the name of the person, the image of the person, or the 'head and shoulders' image you will see other options in the Info button. Touching on this will summon up the Contact entry for the caller.