can i seeif someones reading my texts messages
I'd say to just go through all of your installed apps and see if anything looks suspicious. The only way someone could be reading your text messages without having your phone in their hand is if they installed some sort of spy app on your phone.
Go to your phone's main settings menu, then look for the "Application Manager" entry and find the "Downloaded" tab. Scroll through that list and uninstall anything that looks like it might be an app that could spy on you.
EDIT: It just occurred to me that you might be asking how to prevent government agencies like the NSA from reading your texts. If that's the case, there's really nothing you can do. Your carrier is always going to have access to your text messages, since the messages are being sent over your carrier's network. Any government agency with a subpoena can get your SMS records from your carrier, and there's nothing you can do to stop them.
If you went with an IP-based messaging service like Hangouts or WhatsApp instead of the SMS-based texting that is available through your carrier, your messages would be a tiny bit harder to track. But again, the government could just subpoena Google or WhatsApp, Inc. to get a copy of your records, so my only advice here is to just not send text messages that you wouldn't want a government agency reading.