To make sure it's a problem caused by the software, restart your iPhone (turn it off and on again).
Also, check for a carrier update, if that's possible. Go to Settings - General - About. If a carrier update is available, you'll get a popup asking you to update carrier settings.
If that doesn't help, reset network settings (Settings - General - Reset). This will remove every information about networks set up on your iPhone (Wi-Fi, Bluetooth, ...), and you'll have to set it up again.
Remove your SIM card, and insert it again.
Restoring would be the last solution for a software problem
If your iPhone keeps searching for a network, it might be necessary to repair your device (hardware issue).