I want to design a website that can send and receive sms.
You can take a look at Kannel. It's so simple to create SMS services using it. Just define a keyword, then put in the URL to which the incoming SMS request will be routed (you'll get the info such as mobile number and SMS text in query string parameters), then whatever output your web script generates (you can use any web scripting/language/platform) will be sent back to the sender.
It's simple to test. You can use your own PC and just use the fakesmsc "SMS center" and just send it HTTP requests. If you have a GSM modem you can use that too, utilising the modem's AT command set.