Hello fellow Caitlyn players!
My name is PitouMeow, obviously, and I am a dirty Caitlyn main. I am currently Platinum 3, in my series, and climbing fast. I have played Caitlyn A LOT ever since her rework in November of 2015. Season 6 and 7 combined, I have over 600 games on her plus games I have played on other accounts. I would consider myself a seasoned Caitlyn player and I would like to share some knowledge with you all. For this guide, I will be aiming for an audience of beginner/novice Caitlyn players and maybe some Caitlyn mains will find something they didn't know! I will be putting text in bold and italics that I feel is important to know and for clarity reasons.
For the record, I am aware there is a section to the side that links builds/guides but I thought I'd post this here because a lot of people only look at posts, including me. Who knows, maybe I'll end up posting this on SummonerSchool if it's well received.
I will be posting a lot of Imgur links for reasons relating to character limits. I don't know how long this will be

To start off, here is a link to a post I submitted not long ago about what the recent changes mean for Caitlyn. This will help me by not having to explain it again and clear up some questions/concerns you might have.

What will be in this guide?
* Short Explanation on Caitlyn's Role In The Game and How Her Laning Phase Should Be
* Runes and Masteries
* Starting Items
* Essential First Items and Different Build Routes/Full Builds
* What Abilities To Max
* Simple Explanation of Caitlyn's Abilities and Some Tips * Matchups
* Some Simple Combos
Lets get started. :)

Caitlyn's Role in The Game and How Laning Phase Should Be Played
Caitlyn's role as an ADC is quite unique and painful to deal with. Luckily and sadly, the recent changes made to her and Runaan's made it so she's not a pain in the neck, or at least not as much as she was. Caitlyn is a lane bully, which means she pokes the enemy down, pushes lane like a madwoman and should force the enemy jungler to stick around bot or else they will lose badly or lose their turret early, which opens up possibilities for your team to get stuff done on the otherside of the map, like get rift herald without any contest for it. Since Caitlyn is such a big lane bully, she can even hang with Draven, the best early game ADC there is, which is really saying something. With that being said, it means she can be blind picked against any enemy ADC and do fine since she's such a force to deal with.
Although Caitlyn is a massive lane bully, she's also the safest ADC to pick, other than Ezreal/Lucian, which makes it even easier to blind pick her into anything. Caitlyn can be played aggressively or passively, depending on your style, however, she is a much better aggressive ADC than a passive one, in MOST situations. During and after laning phase, Caitlyn is the BEST objective taker, compared to other ADCs. The sooner you get your turret, the better. Once you do, roam to dragon, mid lane or top lane and pressure those lanes, get the towers and proceed to the next objective. Many people in low elo believe that she's about damage but that's only half true. With her having such a safe kit and range, this makes it easy to roam and get objectives, which is much better than doing a lot of damage. You can do the most damage in the game but if you don't get objective, you just won't win. This goes for everyone, not just ADCs. It's not team deathmatch.

Now that I explained her strengths, and basically how her lane phase is, I will explain a bit more about her entire lane phase should be played. This is REALLY important, it can change the outcome of the game, so bare with me.
Once you get into game, leash if you need too and get to lane ASAP, unless there's extreme circumstances where there's an invade or early fight. You need to get to lane ASAP because the more XP you miss from not being near dying minions, the more likely you are to lose lane and this goes for ANY lane not just ADC. Don't be scared to miss CS, just make sure you get the XP from being near dying minions, dying for CS is not worth at all so keep that in mind.
Against almost any ADC, with exception to Draven, Lucian and Xayah, you have the strongest early game levels, especially if you take fervor but we'll take about that later. Once you get to lane, make sure to CS but also poke because you have the longest range out of every ADC. To poke efficiently use your Q, Piltover Peacemaker, but make sure you hit the entire wave AND the enemy laners. This lets you deal damage to the enemy AND push the lane, which is the most important part about Caitlyn's role as a champion. There are exceptions of course, like securing a kill and such but usually you want to Q the wave AND the enemy. This is even more important now because of the Runaan's change (See link above). Another way to poke efficiently is, whenever the enemy laner's step up to auto attack minions, hit them with an auto and back up. You don't have to back up if you're able to chase and get a kill but it's always better to make sure you don't die rather than chase for a kill. Althought those are only two examples of poking the enemy laners and pushing the wave, it is EXTREMELY beneficial if you constantly do it and pressure them. Caitlyn is really good at whittling down the enemy champions and forcing them to fold.
Since this is a simple guide to Caitlyn, I will end it there because that's literally all you need to know and do to climb with Caitlyn. It's extremely efficient and very annoying.

Runes and Masteries