Welcome to my Graves guide! This will hopefully help you in your quest to be the best League of Legends player you can be.
I am a 1300 Elo player on NA server who currently has a 100% winrate with Graves in ranked play (less than 10 ranked games with him, but he's still one of my best champions).
Pros / Cons
Graves is quite tanky as AD carries go due to his passive, thus he excels in fighting other AD carries 1 on 1 and has more survivability in team fights.
Huge AOE damage from ultimate and Q.
Smokescreen can really help out so enemies can't chase you as easily.
Great attack speed steroid that also gives you a gap closer and escape tool.
Kickass Mafia skin
Lowish range as AD carries go.
No hard CC (only a slow on the W)
This is pretty much the ideal runes for any AD carry. This setup will maximize your early damage and armour so you can effectively trade with the enemy AD carry, while allowing you to have more MR late game through MR/lvl glyphs. If you are facing an AD carry such as Corki that has high magic damage output spells early, flat MR glyphs would be helpful to pick up.
These masteries will maximize your damage output as well as giving you some extra mana and mana regen so that you can cast your abilities more often. You will be hitting the opposing AD carry with quite a bit of force and should be able to out-trade them if you play smartly.
I prefer to start with boots and 3 pots, as it will allow you more sustain and escapability while in lane. If you are paired with a heavy sustain support like Soraka, you can choose to start with a Doran's Blade, but boots and pots is the best all around start for AD carries. Many people would advise skipping Doran's Blades to get a faster Infinity Edge or Bloodthirster, but these people are flat out wrong. The ONLY time you ever want to skip the Doran's Blades is if you manage to get over 2k before going back (and not just from sitting in lane forever with a Soraka) from getting a few kills. Even then I would advise getting 1 Doran's Blade. The reason for this is they are extremely cost efficient, and provide lifesteal and HP needed to increase your sustain. A B.F. Sword will give you higher damage, but the Berserker's Greaves attack speed increase as well as the HP from the Dorans will allow you to out-trade as well as sustain for longer.
I find it best for the laning phase to never leave base without at least 2 HP pots. This will help you to sustain and stay in lane longer allowing you to farm more efficiently. This is just personal preference, so if you want to stay away from HP pots go right ahead.
Bloodthirster vs I Edge
In my opinion, I edge first is better in the current meta. The critical hit doing 250% alone is amazing, and then it gives you a ton of damage to hit hard. My recommended method is to get a Vampiric Sceptre after your 2 Doran's and your Berserker's Greaves, and then build the Infinity Edge. This will give you the sustain from the lifesteal, but it will also give you the benefits of Infinity Edge earlier. This will allow you to team fight more effectively. After the Infinity Edge I go for a Phantom Dancer to give massive attack speed and even more crit chance. Bloodthirster comes next to add a ton of sustain and damage.
Always try to stack up your Bloodthirster as soon as possible. If you are all grouped up in mid doing a dance as you wait for a team fight, tell your team, "I need to stack my BT, let me get the cs please." You need to get it fully stacked to become the true terror that AD carries (Graves in this case) are meant to be.
Last Whisper is another must buy for AD carries, but you should be tailoring your build to your opponents. If your opponents are getting a ton of armour early, get your Last Whisper earlier so you can pound right through their armour.
The last item is really up to you. I prefer the QuickSilver Sash as it gives cheap magic resist and has a great active. It is extremely useful vs champions like Morgana and Ashe who have a stun or bind, and when you activate it will immediately free you from the suppression. Note that this does not free you from spells such as Warwick's ultimate. If the enemy team is really heavy AD or their AP isn't doing quite as well, consider getting some form of armour such as a Guardian's Angel.
Max R whenever you can, and you want to max Q first to get the most burst damage. I prefer to take W at lvl 4 and lvl 8 because lvl 2 W will allow you to 1 shot the caster minions with a Buckshot Smokescreen combo. After that, max your E 2nd as it will give you a huge attack speed steroid and gives you a nifty repositioning tool.
I pick ignite because Graves has relatively low range and likes to get in the opponent's face to deal a ton of damage. Flash is just a great all around spell for escaping and positioning yourself in team fights.
You could also consider Cleanse or Heal instead of Ignite, but as Graves likes to get in their face I prefer Ignite to Heal. Cleanse is quite nice against a team with lots of CC, so if facing an Ashe you might want to consider it as it will allow you to escape from her stun of her ultimate.
Early game, you should try to not touch the creeps until the last hit. You don't want to push your lane, or you will leave yourself more open to ganks. You usually want the lane to be near the middle, but a little towards your side is also nice. If you let the lane get too close to your turret it will make it harder to last hit the minions, so keep it away from your turret but no further than the middle of the lane. When you want to leave your lane (either to go back to buy or to go to dragon etc.) push out your lane. What I mean by that is kill the wave of creeps ASAP so that it shifts towards the enemy turret. This will allow you to not lose any CS to your turret, and will mean that if the opponent goes back they will lose farm.
Once you get into later in the game, you can clear the waves quickly using your buckshot and smokescreen with a few auto attacks for the melee minions. Clearing the waves quickly can allow you to have a little more control over dragon, or even to push the turret.
AD carries are really all about positioning. You want to keep yourself as far away from the centre of the action as you can, while staying in range to do your full DPS. Ideally you want to be hitting squishiest targets first (start with their AD carry, then AP, etc.) but you won't always be in range of them. Anyone who says never shoot the tank is dead wrong. Your job as AD carry is to ALWAYS BE SHOOTING SOMEONE. Shoot whoever is in range of you, prioritizing squishy targets. While you are taking shots at whoever is closest, try to reposition yourself in between shots to get at the squishier targets. If an enemy bruiser such as Olaf runs at you, don't be afraid. Just try to kite him as much as you can, using your E to give you some distance and flashing over walls to get away. Your team should be in between you and their bruiser so by the time they get to you they should have lost a lot of HP. If you can, kill them and then go back to looking for squishy targets.
This may seem like a lot to do at a time, but it's really just all common sense. You want to throw out your ultimate such that it does the most damage to as many people as possible, and use your buckshot and smokescreen to deal AOE damage and blind enemies. Do not be afraid to use your E to chase, and even when you are just shooting from outside the fight use your E to give you a huge attack speed buff.
If you play Graves well, he can be one of the strongest AD carries in the game, and is really one of the strongest champions in the League of Legends.