In which phases of flight should the carb heat be turned on?
Carburettor icing is rare at high RPMs, as there will not be much of a venturi effect. To have carburettor icing in such a scenario, it would have to be very cold and very humid/wet, in which case you would probably also encounter airframe icing, and might want to reconsider your flight. 

Applying carby heat has two downsides:


The air will be unfiltered, meaning dirt or other contaminants can be sucked into the engine;
More importantly, the warm air means you won't be able to reach your usual maximum RPM. 


These are two undesirable traits for takeoff. 

The POH in a Cessna 172 I fly says to have carburettor heat off for takeoff and landing, but only really says it should be on when you suspect icing. I was taught to be much more conservative - prevention is better than cure. I apply carby heat whenever the RPM is below the 'green range', unless it is especially hot and dry outside. However, I remove it when I'm about 30 seconds from landing, in case I need that extra power for a go-around. You also shouldn't apply it 'half way'. Either it's all in or all out. 

Boldmethod has a good article on why it's important, and you should pay attention to the conditions where it is most likely to occur.