Honestly, who doesn't want to play as a bouncy little ninja who can throw shurikans with the greatest of accuracy? Genji can do that, and more, and is seriously fun to play once you get the hang of him.
Main attack/alternate fire.
Genji's main attack is a highly accurate shurikan through. If you can see a target, you can hit it, there is no drop to these projectiles and they will always strike the place you aim them at. These can be absolutely devastating to a target if you hit the head, because it's not just one head shot but very likely three in a row. The alternate fire of this is that he throws the shurikans all at the same time rather than in quick succession, and they will fan out in front of you. This can be useful for hitting up close targets, the bigger they are the more shurikans will hit them, so is great for dealing with tanks.
Genji's Swift Strike.
This is a very versatile move that can be used for a variety of purposes. When you use this, you will dash straight forward and damage anything in your path. Beware, this ability can send you over a cliff to your death if you aren't careful. Also, keep in mind that any time you score an elimination, even if you don't deal the killing blow, the cool down on this ability will be reset and you can use it again immediately. This is important to remember because you can use it both as an engaging attack, and as an escape after you have gotten the kill. The strike is not a straight horizontal one, but will go straight in the direction you are looking, so you can use this as an extra jump even to get to hard to reach places. Not that anywhere is really hard to reach for Genji, but something to keep in mind.
Genji's Deflect.
This is probably one of the most potentially devastating abilities Genji can utilize against stationary targets like Bastion or Torbjorn turrets. When this ability is used you will deflect any ranged attacks that would hit you otherwise and redirect them back to where you are aiming. This can be incredibly deadly if multiple people from the enemy team are shooting at you, as you should be able to just stand still and take the shots, and redirect them to eliminate some of the enemy team.
Genji's Ultimate.
Genji's ultimate can absolutely devastate the back lines of the enemy team. Pick off healers, snipers, and anyone else you can get into melee range of really. He will unsheath his dragon katana and his basic attack will change from his shurikans to a slash with this sword. If you can get the drop on their team from a direction they don't expect you from you should be able to take down two or three of them if they are bunched up easily before they can even turn to face you.
Genji's Passive.
This is the ability that makes Genji, Genji. It grants him the mobility he needs to get in and get out and travel the map quickly with ease so he can sneak behind the enemy position. It's actually two abilities in one, the first being his double jump. This lets him get up practically as high as Pharah, as often as he wants, there's no cooldown time for this. On top of the amazing mobility the jump provides, you also get the ability to run up walls. You can use this to get up on any roof you want, and them from there you can jump from roof to roof if you wanted to. Effectively going up and over the enemy team to drop in behind them, a great way to use your ultimate.
All in all, Genji can be a lot of fun to play. Keep in mind he can be very squishy though, so going all in with his ultimate can be a very risky business if they've seen you coming. The trick to playing Genji effectively is going to be stealth.
Main attack/alternate fire.
Genji's main attack is a highly accurate shurikan through. If you can see a target, you can hit it, there is no drop to these projectiles and they will always strike the place you aim them at. These can be absolutely devastating to a target if you hit the head, because it's not just one head shot but very likely three in a row. The alternate fire of this is that he throws the shurikans all at the same time rather than in quick succession, and they will fan out in front of you. This can be useful for hitting up close targets, the bigger they are the more shurikans will hit them, so is great for dealing with tanks.
Genji's Swift Strike.
This is a very versatile move that can be used for a variety of purposes. When you use this, you will dash straight forward and damage anything in your path. Beware, this ability can send you over a cliff to your death if you aren't careful. Also, keep in mind that any time you score an elimination, even if you don't deal the killing blow, the cool down on this ability will be reset and you can use it again immediately. This is important to remember because you can use it both as an engaging attack, and as an escape after you have gotten the kill. The strike is not a straight horizontal one, but will go straight in the direction you are looking, so you can use this as an extra jump even to get to hard to reach places. Not that anywhere is really hard to reach for Genji, but something to keep in mind.
Genji's Deflect.
This is probably one of the most potentially devastating abilities Genji can utilize against stationary targets like Bastion or Torbjorn turrets. When this ability is used you will deflect any ranged attacks that would hit you otherwise and redirect them back to where you are aiming. This can be incredibly deadly if multiple people from the enemy team are shooting at you, as you should be able to just stand still and take the shots, and redirect them to eliminate some of the enemy team.
Genji's Ultimate.
Genji's ultimate can absolutely devastate the back lines of the enemy team. Pick off healers, snipers, and anyone else you can get into melee range of really. He will unsheath his dragon katana and his basic attack will change from his shurikans to a slash with this sword. If you can get the drop on their team from a direction they don't expect you from you should be able to take down two or three of them if they are bunched up easily before they can even turn to face you.
Genji's Passive.
This is the ability that makes Genji, Genji. It grants him the mobility he needs to get in and get out and travel the map quickly with ease so he can sneak behind the enemy position. It's actually two abilities in one, the first being his double jump. This lets him get up practically as high as Pharah, as often as he wants, there's no cooldown time for this. On top of the amazing mobility the jump provides, you also get the ability to run up walls. You can use this to get up on any roof you want, and them from there you can jump from roof to roof if you wanted to. Effectively going up and over the enemy team to drop in behind them, a great way to use your ultimate.
All in all, Genji can be a lot of fun to play. Keep in mind he can be very squishy though, so going all in with his ultimate can be a very risky business if they've seen you coming. The trick to playing Genji effectively is going to be stealth.