Are you using the "Messages" app that came with your iPad? If so, make sure that the number or email you are sending these messages to also have this "Messages" app.
Remember iMessage only works with iPhones, iPods, iPads running iOS5 and Macs runing Mountian Lion.
It’s always a pleasure to speak with another iPad owner! I don’t need to mention how amazingly versatile and functional it is as I’m sure that you have already experienced it! May I ask what error message are you getting when you are trying to send a text message? Are you using a 3rd party messaging app or are you using the stock messaging app. Also, what make and model device are you sending the messages to? The information that edgarrios stated is a great start on how to troubleshoot this issue. If you are still experience issues with sending texts from your iPad then please advise as I am eager to assist!
Follow us on Twitter @VZWSupport
I'd to jump in this conversation. For me the issue is how do I text to the other phones in my plan that are not Apple products? (using my unlimited texting)