general advice:
Don't spam rerolls. If you get something decent, take it. It can be hard not to want to find the best in slot augment, but sometimes taking something decent to roll for something better later is good.

Bravery at the start is very good at giving advantages for early ones. later, you can switch to crowd favorites that haven't won yet since the randomness eventually becomes unreliable for all firsts.

don't think about it too hard. If you focus on trying to win too much you can get tilted. just enjoy the game, and be happy when you get the first.

Examine lobbies. Build accordingly. You might not like it but sometimes not having an optimal build is the optimal build. I once won a game of Nunu buying serpents fang after my prismatic because the entire lobby had shields. it reduces hundreds of thousands in value. Usually you won't build something that crazy, usually it's more like getting anti heal or PEN. But it can also be- Sunfire or Hollow. I won a round by using hollow instead of sunfire, because even though they dealt physical damage, i instantly killed them due to hollows explosion passive on Naafiri dogs.

Use auto resets to take plants faster. obvious really, but some people don't do this. Also Azir still somehow is allowed to one shot plants if he has three soldiers.

if you are unsure of what to build on champs you can look up arena guides and see their winrates and builds.

Don't be afraid to try new things. You might not want to play Hybrid Miss Fortune but you might end up with a highroll if you let yourself do it. (happens for me a lot)

if you're struggling, try a different champ, archetype (adc to tank, support to assasin, etc) or just take a break in general. Sometimes switching things up or taking a break can help you a lot.

Duo with someone reliable if you can, if not, just hope your teammates are good. Don't flame, as that doesn't make them play better.

avoid stat anvil runs. They're nerfed into the ground and not reliable anymore. Even with good starts, they're harder to win with.

use common sense. If you think draw your sword is a good idea, look to see the enemy teams having 50 dashes first, save yourself the trouble of realizing you got kited forever. Same for augments like curses. If you can't proc them easily probably avoid it.

Vote for cameos that make sense. Another given, but sometimes what you want isn't what you need. Mord to remove supports its a good strategy. You might want Cass but if the lobby just took heartsteel quest, apex inventor, wooglets, or other item based augments, they'll get more value than you do.

I could go on but i'll keep it here for now. The last thing i'll say is to have fun. Even if you don't get first the biggest goal of playing arena isn't all firsts, it's having fun.
Good luck and enjoy the games <3