mbobinger:
How does a switch mode solution work? Are there maybe any tutorials?
Very complicated and not for the beginner [in fact, in many ways it's over my head, too [I'm more of an MCU/blinky lights guy] -- better to find an off-the-shelf solution.
mbobinger:
Would it also be possible to use a voltage regulator with a lower dropout voltage to increase the efficiency?
Perhaps, but even a Low DropOut [LDO] regulator will not guarantee low dropout. LDO merely means as-low-as-it-can-go. If the input voltage to output voltage ratio, is higher than the LDO voltage, there will still be a high dropout voltage.
For instance: Let's say we use a 5V LDO Regulator IC with a rated minimum dropout voltage of 300mV, but, we put a 12V voltage on it's input. The actual dropout voltage will be: 12V - 5V = 7V! So, what's the point of an LDO? -- you might ask. Here's another example that should clear that right up:
Suppose we want to run a device at 5V, using 4 AA cells. And we want to squeeze as much juice [thank you Ben] out of those cells as possible, like still get 5V out of our regulator even when the cells are down to 1.3V...well -- lets do the math!
1.3V * 4 = 5.2V
So, if we use an LDO regulator with a 200mV minimum dropout voltage, or better [like an LD2981CU50TR], then HA!-HA! It can happen!