Welcome to my first ever build! I'll be covering how I build Graves, whom in the recent weeks has become my main. Although this build might be a little strange to start, bear with me, as it personally brings me great success. Enjoy!

Standard runes really. Armor for bot lane dominance and the rest into either Armor Pen or Damage. AD blues can be subbed out for Magic Resist but I don't see the point when the main damage dealer in bot lane is the AD and most junglers are also AD; IMO (in my opinion) might as well have a bit more damage.

I go with a standard 21-9-0 build. Although you could do just fine with a 21-0-9 or ever 24-6 (putting 3 into the Life steal mastery). I personally recommend 21-0-9 as the extra health not only helps with your lane, but also gives extra AD towards your Atma's.

This is were things take a turn in my build compared to most. I personally go in this order, with a few exceptions depending on the enemy team.
First I start of with Boots of Speed and 3 Health potions in almost in lane. I fine the utility of the movement speed and healing from the health pots much stronger than most lanes. Although, going Doran's Blade when laning with Sona or Soraka isn't a bad idea.
Next trip back I buy either the Doran's Blade or the Boots I didn't pick up previously, then upgrading to Berserker's Greaves.
I find rushing Trinity Force to be the best thing for Graves to do. He gets Health and mana, attack speed, movement speed, crit, the sheen proc, AP for his W (although it's rather weak), the slow + damage from phage. All in all it's a fantastic item for Graves (I usually go zeal - phage - sheen - TF).
After Trinity I grab a Bloodthirster. A good item on any AD, especially since fully stacked it gives the most damage in the game (excluding Sword of the Occult I believe, but don't even go there). Bloodthirster gives great sustain and damage through out the game, always remember to farm farm farm and farm some more, this build is expensive, but wonderful.
Once I complete my Bloodthirster I then head for Warmog's. I usually find myself carrying (duh, the AD carry much?) and because of this you will be focused. Hard. In combination with Bloodthirster, you can sustain a lot of damage while also dealing out tons with your Q, right clicks, and Ult. 'Mogs has saved my *** so many times I can't simply list them here, I find it to be a great item, allowing you to win most 1v1 fights.
Atma's paired with 'Mogs is amazing. you gain armor for a little more sustain, crit which is always nice, and a bunch of AD because of the health from masteries + TF + mogs. Altogether Atmogs on Graves is amazing. Don't knock it 'till you try it.
Here comes a tough decision for me. Usually the enemy team will have LOOOOOOOADS of armor so you'll definitely need to pick up a Last Whisperer. Although, in some cases LW is a better buy before 'mogs if you simply can't do enough damage. Frozen mallet is a very nice buy here if they don't have too much armor, more health means more AD plus the AD it gives anyway, it pains me that I can't build it here, but I almost always have LW. Madreds is another option if they're stacking health, again, usually have to sub out 'mogs if so. Infinety's is the bread and butter of any AD carry but I don't see a spot for Graves in this build. I've tried many builds, almost all with IE, and I just don't have the same results that I have with AtMogs.

This is another interesting choice.
I definitely recommend flash and heal over any other summoners but I can understand some others. (You want heal as the AD carry because it gives more HP back to you, allowing you to survive most low level and later fights.) Exhaust is a solid option, but heal seems far superior to me as it gives you more time in lane to farm farm FARM!
Usable Summoners:
Flash
Ghost
Heal
Exhaust
Cleanse
Ignite
I don't see much point in others.

Thanks for checking this guide out! As I said, this is my first guide and I hope you all take it well. I don't exactly know how to link items, summoners, and all those so any tips would be greatly appreciated!

Feedback is always welcome, good luck on the Fields of Justice, summoners!