If you are switching from iOS/iPhone, ensure you disable iMessage & Facetime before removing the SIM from your old phone. Failing to complete this step will cause issues receiving texts. If you're having issues receiving texts, you may need to deregister your phone number with apple. Group chats will need to be recreated.
Transfer SIM Card/Phone Service - Simply remove the SIM card from you existing phone and insert the SIM in your new phone. Included in your box is a metal tool to help remove the SIM Card. Something like a paper-clip will also work.
The location of the SIM card tray varies, but is generally on the left side or under sider. Look for a very small hole on the side of the phone. Press the tip of the tool into the hole to eject the SIM Tray. Once the SIM card tray from your old phone pops out, just go ahead and remove the actual SIM card from it.
Now you can proceed to put the actual SIM card into the card tray of your new phone. The SIM card should only fit one direction - look for the missing corner on the SIM card & in the SIM tray for help. It should fit perfectly snug and slide into the phone smoothly - don't force it!
Note: Most phone nowadays use the Nano SIM format. If your SIM card is too large, you may be able to breakaway a layer.
Note: Google Pixel phones do not have a removable back. You must use the SIM tray.