The power distribution on a board is essential to it running properly. The 5v needs to go into 3.3v and probably 1.2-1.8v as well. You need to make sure that any loads on the power net won't cause a momentary voltage drop below any component's tolerance. You also want to make sure that the components on the far end of the board will receive the same voltage that everything else is receiving. Next you want to make sure that any digital chips won't inject noise on the line and have their own power reserve via decoupling caps. These capacitors need to be speced out to block specific frequencies and placed accordingly. Also, grounding is super important to consider as you want to have a stable "0V" reference (for digital only designs this means having a dedicated ground plane, mixed analog and digital can have separate ground planes).
Now, for most hobbyist designs the rule of thumb is use a simple LDO and the recommended input/output caps (1-10uF) for it and use wide traces to route the power in a star like fashion. Also put a 100nF capacitor next to each power pin for noise and to serve as a power reserve.
More complicated circuits / circuits that will need to go through FCC will require more complicated power distributions. Most professional boards (with high frequency signals on it) that will meet FCC will be 4+ layers, with a dedicated ground and power planes. A PCB I just designed with an FPGA on it had something like 50 capacitors for just the 1 chip, with physical size requirements for each type (the smallest capacitors were 1mm x 0.5mm to block the highest frequency noise, anything bigger won't be as effective).
Don't let this deter you however, looking back on my first schematic/PCB designs I'm amazed at how much better I've gotten. Microcontroller designs with a few chips are very, very lenient. If you mess something up it will likely still work, but your performance won't be as good (i.e. if you use a built in ADC it may not be as accurate, or you might not be able to reliable run it at it's max clock speed)
I forgot about that part, I was thinking back to my experiences at a hardware startup. The battery circuitry was only a small portion of the board, but it was the most complicated electrically.
Yeah, in the simplest case you can battery power a pi with one of those rechargable battery-pack usb chargers meant for cellphones. Those require absolutely zero technical skill, start around $20, and it looks like they can power a pi from a few hours to more than 10.
