Easiest method:
usually this just involves opening up the phone app (where you would normally just make a call), then enter *#06# into the keypad, which will then display the 15-digit number.

In Settings:
iPhone: Settings -> General -> About
Samsung/Android: Settings -> About phone

iPhone in setup mode:
on the Start/Hello screen on your iPhone, usually at the bottom of the screen there is a small Question Mark icon or even a small 'i' (information) icon. Tap that and it should then display the IMEI number.

iPhone on AppleID:
login to https://appleid.apple.com/ and select Devices from the menu. Where your device is listed, click on the device and the IMEI will be displayed (along with lots of other info).

Android device thro' Google:
login to https://www.google.com/android/find and where your phone is listed there is a small 'i' icon adjacent to the phone model. Click on that and it will display the IMEI.

Other ways:
if you re unable to get into the phone at all (and I would ask the question now, why are you even bothering to get it unlocked?), then sometimes the IMEI is written on the back of the phone, or even written on the SIM tray/holder.