First ensure through your network provider that the new SIM card has been activated. If not wait for the activation to complete. Everything will be fine.
If the activation has been completed and still if it doesn't work, Insert your SIM card into any other active mobile phone and check whether it works with it. If it doesn't work there is some problem with your SIM card. Contact the seller where you bought your SIM card. If it works fine with the other phone, then there must be some problem with your new phone's SIM port.
Try inserting any other active SIM card to your phone and check whether the SIM port of your mobile phone is fine.
Also make sure that the new phone is free from network restriction or locked to same network of your new SIM card. If it has been locked to some other network, you need to unlock your device.
To unlock a mobile phone from network restriction, you need to enter it's unique unlock code. You can get an unlock code from the respective network provider or from any private service. For example, If you have a Blackberry phone, You can visit UnBBLock.Com
to get the unlock code. If you have any other model phone, visit http://www.mobile-unlocker.com/ to get the unlock code at affordable cost with easy unlocking guide. Good luck.