I recently recieved a BSA Radiant 3x9x40IR rifle scope with no manual. How do you turn the power on/off or do you have to remove the battery?

Most, by far, the majority of these types of scopes with electronice dots, or other enhancements requiring a battery are turned off when you return the power setting to zero ( 0 )
This is regardless of the manufacturer.

And almost all of the time the power control is integrated in to either the top or side turret, or adjustment knob.

Also most of the time the battery is a # 2032 which is flat and about the shape of a quarter / $.25.00. They last indefinitley until you forget to turn off the power!

hope this helps!