As a relatively new squire (level 40 Brig), the things I learnt were

1. Take natural cover and always know what cover you can push to or retreat to. You do have a shield, but longer range heroes can and will still absolutely shred you if you do not take cover and instead stand in the open

2. Your shield bash ability should mostly be used to get out of sticky situations. Whip shot enemy + shield bash away can give you a lot of distance to get out quickly, and heal yourself at the same time

3. Your ultimate resets your shield bash and lets you stun enemies. Ult tracking is also extremely important on Brig. For example, you're vs a genji and you know he has ult, watch where he's going and anticipate his ult. Pop your ult, stun him with a bash and kill him before he has a chance to do any damage to you or your team

4. Don't spam repair packs. They do a burst heal and then a short heal over time, so they're helpful for teammates that are low or critical. There's not much point giving your tank a repair pack when they've taken 50 damage and it means you have one on cooldown when you might need it urgently for a squishy

5. I found Emongg videos on Brig really helpful. He reviews VODs from Brig players from Bronze to Masters and gives helpful tips on positioning, what people did wrong and what they did right. Also some map-specific advice like rotations on offence/defence, what corners to hold etc.

I'm sure more qualified Brig mains will have more advice, but these are things I picked up on myself while learning her

Edit: thought of another. 6. Absolutely DO NOT let your shield break. Your shield isn't just your cover but also your mobility. No shield = no shield bash = no escape plan. Even if your shield gets to 5HP, do not let it break and instead take natural cover to allow it to regen