The problem#
I recently helped a friend with building a computer. While there's plenty of guides online, I thought I'd write down my own thoughts of everything I was considering for this recent computer build.
The intended use of the computer was as an inexpensive but expandable gaming PC. Meaning it should be able to comfortably play relatively recent games at an acceptable framerate, but not at max settings. And hopefully that should continue to be true for at least a year or two. And when it does get to be too underpowered for even low-end gaming, it should be possible to fix that by replacing parts, not the entire computer.
The solution#
Most of planning a computer build is using PCPartPicker and NewEgg to search for the components and NewEgg and Tom's Hardware for reviews (the former for specific components, the latter for selecting things like how powerful a CPU/GPU you need).
I am intentionally avoiding specific component recommendations in this post because those would be out-of-date pretty much immediately.
The PCPartPicker interface will guide you to what categories of components you will need, and help you determine which parts are compatible with each other. The required components for a functioning computer are a motherboard, a CPU (and cooler if not included), memory (RAM), and a power supply. You will almost always also want storage (an SSD), a case, and additional cooling (usually fans to install in the case). Most of the time you will also want a video card (GPU), but modern processors often have a very underpowered one built-in, which is usually sufficient if you aren't playing games or otherwise using a GPU.
Note that I am not including peripherals. To actually use the computer, you will probably want a keyboard, mouse, monitor, and possibly speakers. But those are easily moved among different computers.