Widowmaker isn't an easy hero to play, and will generally require either a lot of practice, or a lot of play time with other games where you have played a sniper. If you can effectively nail those head shots though, Widowmaker is incredibly deadly and very frustrating to be up against.
Widow's Kiss
The Widow's Kiss has two modes of fire, assault rifle and sniper rifle modes, by default your main fire is the assault rifle. This can be great for when a Genji or Tracer gets the drop on you, as it gives you a chance to fight back against these incredibly fast heroes. It isn't much, but it's something at least. You won't be relying on the assault rifle mode much though, as the main mode you want is the alternate fire sniper mode. Holding the alternate fire button down will bring up the scope of the rifle, and the longer you look down the scope before taking a shot, the more damage it will do. You'll see this represented below your target as a percentage of power, it is best to build this up before every shot so that you can make each shot count.
Grappling Hook
This ability gives Widowmaker a deceptive amount of mobility, at first glance it seems like a great tool to get up to a couple harder to reach sniping positions that even Hanzo with his wall climbing couldn't reach, but it can do a lot more than just that. Using this effectively can get you back into a fight faster by swinging from point to point on your way back rather than just running it. Also, you can use it as a quick means of escape if someone sneaks up to your sniper position to catch you off guard. It can take some time to learn all the points you can grapple up to effectively though, so take her out for a spin in some practice matches and really learn the maps, it'll pay off in the long run.
Venom Mine
Found a great sniper point, but there's an easily accessed back way to get to it? Place one of these bad boys and you should be able to get some warning if an enemy is about to sneak up behind you while you are staring down the scope of your rifle. Keep in mind that these things will stick to anything, not just the floor. Place them where the enemy isn't going to see them to destroy them, like on the wall just on the inside of a doorway so they'll run through and set them off, or even on the ceiling. They don't deal much damage on their own, but if you listen for them going off they'll provide you with that warning you need, and a bit of a head start on the fight to come. As a side note, don't place these too close to your actual sniper position, they can hurt you as well if you are caught in the blast.
Ultimate Infra-sight
Widowmaker's ultimate is amazing, and there is no such thing as a wasted ultimate as Widowmaker. This ability will give you and your entire team the ability to see where every member of the enemy team is at all times, through walls and everything. Not only will it spot enemy heroes, but enemy teleporters as well, and knowing where those are placed are the first step you need to destroy them quickly.
At the end of the day, no amount of tips is going to help play Widowmaker if you can't aim and get those head shots though. If you are determined to play her, you are going to need a lot of practice, good luck!
Widow's Kiss
The Widow's Kiss has two modes of fire, assault rifle and sniper rifle modes, by default your main fire is the assault rifle. This can be great for when a Genji or Tracer gets the drop on you, as it gives you a chance to fight back against these incredibly fast heroes. It isn't much, but it's something at least. You won't be relying on the assault rifle mode much though, as the main mode you want is the alternate fire sniper mode. Holding the alternate fire button down will bring up the scope of the rifle, and the longer you look down the scope before taking a shot, the more damage it will do. You'll see this represented below your target as a percentage of power, it is best to build this up before every shot so that you can make each shot count.
Grappling Hook
This ability gives Widowmaker a deceptive amount of mobility, at first glance it seems like a great tool to get up to a couple harder to reach sniping positions that even Hanzo with his wall climbing couldn't reach, but it can do a lot more than just that. Using this effectively can get you back into a fight faster by swinging from point to point on your way back rather than just running it. Also, you can use it as a quick means of escape if someone sneaks up to your sniper position to catch you off guard. It can take some time to learn all the points you can grapple up to effectively though, so take her out for a spin in some practice matches and really learn the maps, it'll pay off in the long run.
Venom Mine
Found a great sniper point, but there's an easily accessed back way to get to it? Place one of these bad boys and you should be able to get some warning if an enemy is about to sneak up behind you while you are staring down the scope of your rifle. Keep in mind that these things will stick to anything, not just the floor. Place them where the enemy isn't going to see them to destroy them, like on the wall just on the inside of a doorway so they'll run through and set them off, or even on the ceiling. They don't deal much damage on their own, but if you listen for them going off they'll provide you with that warning you need, and a bit of a head start on the fight to come. As a side note, don't place these too close to your actual sniper position, they can hurt you as well if you are caught in the blast.
Ultimate Infra-sight
Widowmaker's ultimate is amazing, and there is no such thing as a wasted ultimate as Widowmaker. This ability will give you and your entire team the ability to see where every member of the enemy team is at all times, through walls and everything. Not only will it spot enemy heroes, but enemy teleporters as well, and knowing where those are placed are the first step you need to destroy them quickly.
At the end of the day, no amount of tips is going to help play Widowmaker if you can't aim and get those head shots though. If you are determined to play her, you are going to need a lot of practice, good luck!