Post your games!

post

This is right. You get a feel for what to build depending on what kind of ADC you're playing/how the lane went/team comps etc. as you gain more experience. I'll try to explain them:

Last Whisper: If they're absolutely stacking armor, get this second. If they have armor in general, get it third. If they don't have armor, skip it until they do.

Blade of the Ruined King: If you need self-peel (like if their frontline is able to stick on you and you can't get away even if your team tries to help), if they're stacking health (Warmog's, Sunfire, Randuin's). Generally avoid on champions like Jinx, Caitlyn, and Ashe. Some ADCs absolutely need BoRK (Quinn and Vayne, somtimes Kog and Graves) because it complements some part of their kit (Silver Bolts, Caustic Spittle/Bio-Arcane Barrage) or because they need the burst it provides to win a duel (Graves, Quinn).

Bloodthirster and Infinity Edge: These are the two most common first-item choices you'll see on an ADC, though BT is becoming more popular than IE now. People build BT/IE first because they're huge damage spikes. The difference between them is that BT is more of an immediate damage spike (+100 AD/18% lifesteal at full stacks), and IE is a late-game item, most effective when you have high crit/AS with a Zeal item. BT is a core item on champions that scale hard with AD (Jinx, Varus, Lucian), and IE is a core item on champions with a late-game spike (Tristana, Kog'Maw, Twitch). Some champions can go both ways, depending on the situation (Caitlyn, Ashe).

Zeal: There's not much explaining to do here. Once you have an AD item, Zeal gives you AS/crit that amplifies your DPS. PD/SS is generally preference, but PD > Shiv for DPS and dueling, and Shiv > PD for waveclear/utility/a bit of extra burst in fights.

Trinity Force: Only build this if you're playing an ADC that casts a lot of spells. Ezreal's Q applies instant Sheen, so he becomes bursty as hell after he gets it. Same applies with Corki once he hits level 6. Ezreal is a unique case because of Mystic Shot, but Corki/Lucian use it well because they use their spells a lot. All of these ADCs benefit fully from Tri's odd stats (AP and mana).

There's also the issue of defensive items:

Quicksilver Sash: If you get CCed and are going to die because of it, this gives you a cleanse and lets you avoid that. Because of the nature of ADCs, QSS into Mercurial is usually the best defensive item choice.

Banshee's Veil: Usually a worse choice than QSS, but it's better against hard displacement like Blitz or really good poke like Nidalee.

Randuin's Omen: Mostly for heavy AD comps that want to dive you a lot.

Guardian Angel: If a lot of your damage is up-front and you know you'll die early in a fight, or if your team is a dive comp and can't be bothered to peel for you.

Warmog's: Kha'Zix, Katarina, also if the other team doesn't know what health shred is.

Frozen Mallet: ...you know there's really no reason to get this anymore since BoRK exists, but I guess if you need to kite better.