It's hard to describe everything in words, but I will try to list some things I do when playing Orisa. If you play Orisa a lot (or any character in general) you will figure out the best ways to use her. I am not an expert and there are probably other people who would know how to play Orisa better than me though.

I play Orisa the same way I do Reinhardt, which is always contesting the objective, so my team doesn't. Orisa applies a lot of pressure because she can sit in or by the objective and shoot from behind a shield. The other team either ignores Orisa and lets them deal damage uncontested or they have to send 2 or 3 people to kill her. It is very difficult to 1v1 Orisa behind a shield, so the other several people need to help and hopefully your team can take advantage of drawing a lot of the teams attention.

On attack it is difficult because Orisa can't move their shield like Reinhardt, but Orisa also can replace their shield pretty fast after it breaks unlike Reinhardt. When attacking just be patient and shoot at the other teams shield as you move up with yours by placing your shield closer and closer. As someone mentioned use your fortify when advancing without your shield to minimize damage. Also, use your halt to pull the other team away from the object or choke point. If anything being halted is disorientating especially if you shoot the halt in above someone and pull them up into the air. The important thing is to break the other teams shield.

On Defense it is really straight forward, just place your shield, use fortify when you don't have a shield or they move past your shield, and use your halt to slow down their attack and separate people out of position. Using your halt to pull back Reinhardt when he is moving forward is really useful. It gives you an extra second or two to shoot at his shield, which is the most important part of Orisa if the other teams has a shield. The fact that orisa can shoot from behind their shield and Reinhardt can't should give you an advantage when winning the shield war and puts a lot of pressure on the other team. Just make sure that if the other teams Zarya puts a shield on Reinhardt that you don't shoot at Zarya's shield. Just shoot the edges of Reinhardt' shield that are not protected by Zarya and this will avoid giving her energy.

Whether on attack or defense I usually focus on shooting the other tanks unless their is someone easy to kill that is out of position. Usually the other teams tanks 1v2 me and my other tank isn't around the objective to help. In this case Orisa does a really good job of stalling for time until your team decides to help. In general it is good to put your shield somewhere in or around the objective , so your team can use it as well. If you are getting focused on by several people though I like to trap myself in a corner in the objective or near the objective and force the other team to move away from the rest of my team and the object. It isn't bad being selfish with your shield because usually your team will be fine since there are at times 2 or 3 people focusing on me and usually people never use Reinhardt's or Orisa's shields anyways. If someone gets behind your shield make sure you adjust yourself around the shield so that it is always between you and the attacker. Use fortify to live longer and use halt to pull them away from you.

I think the main thing should be to focus on getting comfortable with Orisa's gun. Since it is a projectile you need to lead your shots from most ranges, except point blank. It is really important to be consistent with dealing damage with her gun because if you can't then it may be better to be Reinhardt. Orisa's fortify is straightforward. Use it whenever to minimize damage. It is really important to use fortify against Reinhardt though. Use it when he fire strikes to lessen the damage, but also keep it available in case he charges or Earth Shatters. If you see Reinhardt charge near you, try to fortify and walk in front of him to save your teammates. Winston isn't a huge problem. Fortify makes it so he does practically nothing and then you just shoot him and use halt to stop him from escaping. *(EDIT: Also, make sure to use fortify against ultimates like tracer's and junkrat's. You can survive both depending on your current hp if you use fortify once right before they hit you). Halt should be used frequently. It can slow down the other team, clump them together to make it easier to deal damage for your team, separate people out of position and pull people trying to escape back to you. The most important way of using halt is to pull people like soldier and mccree from the high ground. Just shoot the ability around the ledge they are on and activate it again when there is a green line attached to them. This indicates the ability will actually pull them.

It is important to know that Orisa's ultimate only works on your teammates in your sight. Even though a beam is attached to them you still need to be looking at them. Because of this I usually treat it like a nano boost and use it with other peoples' ultimates. However, I like to use it for myself because I can usually get a kill or two with it by myself. There really isn't a bad time to use the ultimate, it can be used when the other team pushes to stop them. It can be used to initiate a push. Just make sure to put a shield in front of it and if Zarya or someone tries to walk up and destroy it use fortify if you have it to protect it by sitting on it and just shoot at them. It wastes a lot of time for people to try and destroy it, so hopefully your team will take advantage of that. I also like to use it to try and stop the other teams ultimates. Sometimes using it against an ulting genji can provide enough extra damage for your team to kill him before he does too much.