Q: i lost my iphone and i need to follow up it by serial number but i don't know how to do it.

If you need to find your serial number you can check:

1. The box it came in
2. iTunes, by going to Preferences>Devices and hovering your mouse over the backup
3. http://supportprofile.apple.com, if you ever registered it with Apple.

This won't help you find it, however.  It will only enable you to prove it is yours if it is found, and to inform your insurance company.