I'm sending in my iPhone 4 to trade it in. Is there a sim card or battery that I need to remove first?

Do you mean the Apple recyle program?

If getting rid of it, I would go into Settings, General, Reset, and run "Erase all content and settings".

Then pull the SIM card out (not much on it, but it does have your account info from your old carrier) as nobody else needs that.

If you are getting a new iPhone and want to use this one to set it up, make sure you backup this one before erasing it, so you have your backup file to restore the new one from.

Do not touch battery or attempt to open the iPhone Not user serviceable

It might affect acceptability into the program