The most important point to consider while playing Graves is that you should not play it if you are a duelist. This is because Graves is very good at dealing out high amounts of physical damage, but if you happen to land a critical hit then it can be deadly! Try not to get too close to your opponent, or you will take extra damage.
Here is a quick trick to help you get the most out of your Graves build. At level 10 you can place a soulstone on the bottom side of your grave. When you activate your soul singer, it will create a red beam of light that will cut through any creeps or enemy units in its path. If an enemy gets too close, then the beam will stop and they will be forced to get back into the pit you created. The great thing about this is that the beam can be arranged in such a way that it cuts off all but one path of their movement, making it very hard for them to regroup.
The next thing to note about playing Graves is that you should utilize your quickdraw ability. While Graves is mostly useful for poking and team fighting, the ability to quickly draw a weapon back and forth can be very helpful in ganging up on an enemy or coming up on them from a safer position. Try not to let your opponents know that you have a quickdraw ability, because they will likely use their time to either escape or get back to their safe spot. A great trick is to toss a creep or two onto your opponents when you have Graves next to them, then quickly move into position to deal out a lot of quick damage.
The last thing to note about how to play Graves Runy correctly is to know when to use its powerful rune abilities. Unlike other carries in League of Legends, a Graves player is not allowed to randomly select a spell to use. Instead, each of his or her abilities have a certain time duration in which they will apply their effects, so you must know when to put them on. Using the wrong type of spell when you're fighting a target with a stronger, more resilient team can prove disastrous.
One of the most useful things you can do in the early game is to carefully apply slow, area of effect crowd control spells to take down targets as quickly as possible. A good example of such a spell would be Sunfire Cape. If you're building up a large amount of health, it's wise to use it to finish off a badly dueled opponent. The same goes for a combination of stuns and slow CC, as this combination is extremely effective if you're taking down an enemy that has a lot of mobility.
In the early game, it's also important to keep in mind that Graves is squishy. Try not to fight him in a one-on-one situation unless you're sure you can outlast him. Focus on building up your own health and using your slows to keep him from escaping. When you're able to fight him properly, though, he'll have a very difficult time getting away from you.
At level 15, you'll likely find yourself needing to place more focus on how to play Graves. You'll want to start focusing your zoning in on the middle of his team. Because you are the tank, your job is to soak up damage while the rest of your team regains shields or other forms of damage. When you're at the backline, you'll want to be ready to initiate the most effective engages and follow up with is to close the fight as quickly as possible.
Finally, it's important to remember that Graves is not a "carry" hero. He can build up substantial levels very quickly, but he doesn't do much in the way of "carrying" himself once he's top laner. If you're looking to make a big impact on the game, consider building to support your carries. If you're the best Jungler in the league, roam for kills and go for team kills.