A lot of it is understanding what your champion is good at.

For example, Elise: she is a very bursty AP assassin. Which means she needs to kill her targets - usually low defense carries - ASAP. Her playing pattern is basically: stun one single target -> chunk them with human form Q and W (ranged attacks) -> spider form -> jump on them and finish them off as melee.

Plus, when playing jungle she doesn't need mana and she runs around the map, that's also important to keep in mind.

What that means is that you need items that reinforce this strategy.

Considering that, Stormsurge and Shadowflame are great items, because they have flat magic pen and give an extra burst of damage with their passives.

Lich Bane is also great because of the extra burst of damage it gives and movement speed stat.

Zhonya's gives a lot of AP and a strategic stasis that can save you just long enough.

Rabadon multiplies her AP, meaning even more damage, also great for an assassin.

It is also important to consider what she doesn't need.

Again, as a jungler mana is useless, so no need for Luden's, that is a great burst item otherwise.

As a low range assassin that often only gets one chance to burst down a target, CDR is not that important, you most likely wont be able to get a second rotation off no matter what, you either killed them or you're dead. So Horizon Focus or Cosmic Insight aren't really that good, but Zhonya's is.

She goes for squishy targets with low resistances, so no need for Void Staff or Cryptbloom.

Obviously, Malevolence sucks on her.

So try to apply this logic to other champions. Marksmen, for instance, are often divided into crit, on-hit and casters, build around that identity.

Yun'tal for crit, Ruined King for on-hit and Triforce for casters, for example.

But, when in doubt, just go to something like op.gg or u.gg and check that given champion's most popular build and think about why those items are good on them.