I am looking for a book explained how to make a computer by using Arm core processors?
> and honestly I have no idea how a BGA component is soldered.
You need some form a reflow oven (basically heat the whole board until the solder balls which are part of the BGA package melt). There are some quite fun tutorials using an old household kitchen oven or even a toaster for doing this on the web - but I wouldn't recommend cooking food in the thing afterwards =)
My DIY attempts in the past tended to struggle with boards which are double-sided - things on the bottom of the board have a nasty habit of dropping off. Pesky gravity
> My advice is to start off "small"; play with Cortex-M devices on breadboards to start,
Yep - this is the best advice I've seen. Start small, learn the basics, and then make something a bit more complex for your next project, etc. ... but definitely have a go!
If you have a particular Arm SoC in mind it is always worth checking with the manufacturer of that device - they may be able to share some schematics for a reference board based on their parts.