Using either the 'phone app or the web version you set up and alter a schedule very easily. Our current schedule is very simple. Monday to Friday mornings are routine, Weekends are different. Weekday evenings take account of usually coming home at different times rather than having a single set point for the heating to come on and heat an otherwise unoccupied house. The nice thing is that you can turn the heating on remotely, so for those times when we're coming home earlier than expected a quick tap brings on the heating.
You can also use geo-fencing, but given that I'm often driving past the house I suspect this wouldn't be a useful feature for me! The other thing that Nest does is turn the heating off when no one is home. So, if I have to go off to the gym to do an early lesson, Nest will turn itself down.
Under our old system we had the heating running for around 7 hours a day (5:30-09:00; 17:00-21:30). With the Nest this can drop to around 3.5 hours for some days. That could represent quite a saving over a heating season.
One thing that was hidden away in the features is the pre-heat time. The default setting allows the thermostat to bring the heating system on up to 5 hours before the set temperature. So, if your'e used to having your heating come on at 06:00 to reach your desired temperature by 06:30 you could find that your heating comes on at 01:30 under extreme conditions. Not very likely I know, but you can change this setting. Being a bit old school, I've set ours to a maximum of 1 hour.
At a slight tangent, when you set your temperature you really need to think about where the thermostat is sited and fiddle around with the temperature to get it right for the house. Balancing your heating system can help save money too because overheated rooms wastes energy. When I was working in R&D our design day temperatures were 16 in bedrooms, 22 in bathrooms, 21 in the lounge, and 18 in other living areas. Now without a lot of effort that's pretty difficult to achieve. But doing simple things like adjusting radiators and TRV's to get a more even distribution of heat helps. Our thermostat is in the hall and it's usually set to 19.5. It doesn't matter if it's actually 19.5 in the hall as long as the house is warm.
I suspect the Nest is far more accurate than the old bi-metallic strip thermostat we used to have. That used to be set to 17 because that gave an even distribution of heat. The nice thing about the Nest is that you can tweak the temperature up or down, knowing that in the next cycle it will revert to the previous settings instead of having to remember to reset the stat manually.
Overall I'm pleased we decided to have the Nest installed rather than a programmer and thermostat.