Go to Settings > Messages, where you can:

• Turn iMessage on or off
• Notify others when you've read their messages
• Specify a phone number, Apple ID, or email address to use with Messages
• Show the Subject field
• Block unwanted messages

Manage notifications for messages. See the Basics section -> Alerts and Notifications Center.

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