It's different for texts and other notifications (such as emails, apps, and the sort).
To get notifications at a higher level, there are a few ways. While in any app or media using program, raise the volume on the volume bumper. The other main (and my preferred way) is to go to Settings-> Sound and Display-> Ringer Volume-> then adjust the volume for notifications.
For texts, go to Messaging-> press the Menu button (bottom left corner next to Home)-> select Settings-> then the last section is Notification Settings. Here you will find Select Ringtone, Vibrate and Notifications.
Also, if you have Vibrate or Silent selected from the drop-down menu, no sounds will play.
Hope this helps, it took me a while to figure all that out after trying to change my text notification tone and wondering why my notification volume kept going down.