A few tips for Zarya

Her weapon's main fire is medium-short range, and does rather low-damage initially. Her alt-fire is a grenade which takes an arc path, and does splash damage as well as hit damage. However, Zarya has projected barriers (essentially a shield bubble) that can be applied to herself and her teammates. When these absorb damage, a number on your reticle will begin to go up, from 0-100, which indicates how much your weapon has been boosted. At the 80-100 range, you will absolutely melt most players, just don't get too cocky. This boost constantly decays though, which means that playing Zarya is a delicate dance of trying to bait the enemy into feeding you as much damage as possible, without getting killed.

Half of her health is shield based, not to be confused with the 'projected barrier' shields she places on herself and teammates, this is health that is blue colored, and will actually regenerate on its own outside of combat. This makes Zarya pretty resilient and means that temporarily ducking out of combat to regen can be a lifesaver, and reduces her need for medkits or a healer, although they're still very helpful.

Now for her project barriers, which I will refer to as shields for the sake of ease. Activate your shields as you begin to take damage, rather than preemptively to get a better chance at absorbing damaging to juice you up. If you're against a sniper, reaper or someone who's going to do heavy damage and you want to prevent it, early activation isn't always bad, it's just that doing it too early can cause your shield to run out before you've been attacked (it last longer marginally longer when taking damage, unless it takes enough to be destroyed) and the enemy has a better chance of just deciding not to shoot you.

Also, Zarya's shields can negate many ults when times properly: High Noon, Dva's self destruct, Rip Tire, etc. Just remember to get the timing right. It can also be used to escape Mei's freeze buildup, both from her main weapon and her ult. It can also be activated as a Reinhardt begins to charge at you if you're quick, and instead of dodging you can let him take you while the shield is up to get a 50% juice boost.

Keep in mind the shield can also be destroyed from significant damage, or worn out by certain attacks. An emplaced bastion should not be straight up confronted. Your shields can save you if you need to get out of his firing path, but he'll quickly tear you apart if you aren't smart about it, shields or not. Pharah's justice rain will also take you out if you are under fire for the majority of it, since it lasts like 4 seconds. If you're caught in one, feel free to pop your shields. Just don't try to walk into it thinking you'll get a sweet damage boost.

Remember to shield your teammates as well. This is one of the most important things to remember, and takes Zarya from just being an awesome tank to a truly supportive member of the group. It's obvious that you shield friendlies that are rushing the enemy, taking damage, near death, etc. but remember to also use them in the aforementioned situations as well. For every ult you can save yourself from, you can save another person if you do it properly too. You can even shield a teammate that's already been grappled by Reinhardt in anticipation for the pin.

Now for her ult. Much like her alt-fire, her ult is an arc-path grenade that essentially turns into a gravity well, pulling nearby enemies in and holding them there. Keep in mind it does not disable any of their abilities, and they can still fight back. Rarely try to solo your ult, unless you're heavily juiced and using it on a group of weaker characters maybe. Ideally it should be saved for when your team is present, and even comboed some of their ults, like Death Blossom, Earth Shatter etc.

There's probably more to say, but just playing her enough should help you get the hang of it. Hope this was helpful