Go to Settings > Messages to set options for Messages, including:

• Turning iMessage on or off
• Notifying others when you've read their messages
• Specifying an Apple ID or email address to use with Messages
• SMS and MMS options
• Turning group messaging on or off
• Showing the Subject field
• Showing the character count
• Blocking unwanted messages

Manage notifications for messages. See the Basics section -> Do Not Disturb.

Set the alert sound for incoming text messages. See the Basics section -> Sounds and silence.