So, I do understand that building right is important, I've been playing a while but haven't been able to figure out how to build for each character. I've watched the pro streams and they seem to know what each item does and how it works for each character.

How do they get to that level? Do they just memorize all of the items and their effects, and memorize all of the champions' Stats?

How should I go about getting good at building my champs during games? It seems a bit daunting to me, like constantly studying for a test. haha.

When you start, just try to find a build that is balanced. In most cases, a balanced build is better than an pure offensive or a pure defensive one. Most new players build way too offensive or way too defensive.

After you get some experience with balanced builds, start counter building. If the enemy compose mostly of AD, build more armor. If the enemy compose of mostly AP, build more resist. If the enemy compose mostly of armor, build armor pen or magic damage. If the enemy compose mostly of magic resist, build magic pen or more physical damage.

But for starters, just focused on building a balanced champion.

Understanding how different abilities work is very important. A mage who constantly deals damage to a target (Vladimir or Brand, for example) would utilize Rylai's Crystal Scepter or Liandry's Torment than other champions.

Physical casters ("mages" who rely on attack damage), like Pantheon and Urgot might benefit more out of a Manamune for the consistent mana or a Black Cleaver for the armor penetration than a Tristana.
In terms of survivability, I would suggest you prioritize health over armor or magic resist early on. Many champions (like Tristana or Kayle) use different types of damage. Sometimes a flat number (like 800 health) is more effective than a percentage (like -15% physical damage). This is more true the earlier in the game it is.

Memorization is definitely important. Knowing that Pantheon has a hard time against Renekton might make you decide on getting an Avarice Blade for the additional gold and Vampiric Scepter for the sustainability, but all of that decision making comes with practice.

The important things to think about for your champion:
Do I deal consistent damage, or single-attack bursts?
Do I have any issue with mana?
What kind of gear does the star players on the enemy team have? How can I counter that?
What kind of damage is hurting me the most?