How to minimize battery usage while hatching eggs in Pokemon Go?

The easiest settings to reduce the energy consumption are your Location settings:

->> Settings ->> Location

->> Mode

Here you can choose battery saving which has quite a big influence. Your battery is saved at performance's charge: When I activated the "battery saving" location setting I noticed some huge latencies when walking around whereas I never faced those issues when I played with the "High Accuracy" option.

I think this option is available since Android 5.0. Correct me if I am wrong.

Another option is in the Application's setting itself:

->> Pokemon GO ->> "Pokeball" ->> Settings

I do not know what this option does exactly but I think it also tries to reduce the accesses of Android's Location service (Also look at this topic: What does the battery saver do in Pokémon Go?).

Update June 30, 2016: This Update removed the In-App Battery Saver for iOS.

Tip:

Always carry along a charger and hang around nearby sockets :P

Best is maybe also download the map in google maps for your area? I did this and it seems to improve the battery loss