I think I'd probably work backwards from probuilds. So look up whatever champion, and see what a pro player built on that champion in a particular game, and then try to figure out the 'why' behind each item (and for bonus points, why in that particular order). Sometimes items are situational based on comps, other times certain items in certain orders are simply mathematically more efficient, other times there are playstyle preferences, or other times it may be due to forced back timings. (Note that in some cases, people have actually pulled out spreadsheets to compare DPS of various builds at different points on different champs, so optimal builds aren't always obviously optimal until you do the math.)
It's much easier to look at a champion and be given the 'answer' (as pros are usually going to be building optimally, albeit not always) and then justify it yourself, than try to look at a champion, consider all the items out there, and try to figure out which ones are best. Then once you've figured out why a pro built all the items they did on a certain champion in a certain game, do it again for a different champ. Repeat until most probuilds are more or less intuitively obvious to you.
Then try to figure out builds for champs you didn't look up pro builds for using your now somewhat developed intuition. See how what you comes up with differs from what the pros did, and try to figure out why the difference(s) exist.
Beyond that, you can playtest builds. Don't do it in ranked, but once you've got a pretty good understanding of item builds, anything that you think is worthwhile to test out is probably plausibly viable enough that people in normals won't notice/care. (Note I said once you've got a good understanding of item builds though, theres no reason to 'test' AP Garen for example. People have done it, but they're knowingly trolling and/or taking advantage of the fact their 'true' elo is somewhat higher than the one they're playing at, not actually testing it.)
Paying attention to how pro builds change between patches can also be insightful if you can get a feel for how significant buffs/nerfs are and what sort of rippling effects from even non-item changes can result in changes in item builds.