There are no indicators when it's sent. You are sending it, you know if you sent it. For received texts, you will get a little messaging icon in your notification area.
Firstly as to sending you can turn on Delivery Reports if you want to know if they received your text. This isn't exactly what you were asking but its a very cool feature that a lot of people seem to not be aware of. With this turned on a few seconds after you send a text you will see a little check mark appear next to it. This way people can't say they never got your text
To turn on delivery reports: Messaging >Menu >Settings >Delivery Reports: Check
And then for your incoming alerts: Messaging >Menu >Settings >Notifications: Check, Choose Ringtone, Choose Vibrate.