To turn off your iPhone, hold down the silver button on the very top of the phone until the screen prompts 'slide to power off'. Do as it says and the phone will power down.
To turn your iPhone back on again, simply hold down the same silver button until the Apply logo appears, let go and wait. It takes 30 seconds or so to fully start up.
When your phone is back on, you should then have a signal. If not, you need to think whether you should be expecting a signal where you currently are (mobile coverage is by no means a given, even in this modern age). If you know you should be getting a signal, get in touch with your carrier (the ones who supplied your SIM card) and ask them to check your account/SIM. You will need to know the SIM number (ICCID), found in your iPhone's Settings pages.