My boyfriend and I are using the same Apple ID on both of our phones. I just want know how can I link my phone to his?
Without jailbreak no.
Even if you're using the same Apple ID on both devices, you can't get the same SMS and call (and also call logs) of the other device, because this two things depends from the telephone number and they're recorded on the device that received the message / call.
Probably you'll get the iMessage on both devices because they works differently, so every device logged with the same ID will get all the messages, but deletion are not synchronized.
Apple ID is used to keep settings, app and profile settings synced across Apple devices.