In almost all my games I notice new players make the same set of mistakes over and over which usually costs us the match, so here's some tips that'll hopefully help someone be a better contributor to the team instead of the guy that solo drops and dies two seconds after landing.
*Don't play music or have loud televisions on when you're playing, you can hear enemy movements if you pay attention which can save yourself or your team's lives even.
*You can move while downed and even open or close doors, so if you get downed during a firefight and the enemy isn't able to finish you off take the opportunity to find a building or even a rock to hide behind so any teammates nearby can try to revive you without getting shot in the process.
*Don't overextend from your team, specially at the beginning when you're still looking for weapons and armour. If you overextend there's a good chance you'll get killed and have to start all over again.
*When looting be sure to leave things for your teammates as well, if you open a crate and find two weapons don't just grab both and leave your team unarmed, also ping gear they might need like armour and helmets, you can see what they don't have by opening up your inventory screen and it helps slot to have everyone geared up before you engage the enemy.
*If you're playing someone like Bangalore or Caustic and are trying to retreat, loot or revive a ally use your tactical abilities to obscure enemy vision and reduce your chance of getting shot in the back.
*If you see a enemy don't immediately open fire, ping them and check the surroundings because there's a good chance their friends are nearly so even if you manage to down someone most likely their team would come in, kill you and revive their teammate.
*Learn how the weapons fire by using the training range so you don't use the wrong weapon in the wrong situation, the Havoc and Devotion weapons will almost certainly get you killed in a close quarters situation because of their long charge up times unless you're lucky enough to get a gold tier attachment that reduces the charge time.
*If you're killed don't immediately leave the game, your teammates might try to get your respawn beacon and revive you and when you leave you're putting them at a disadvantage numbers wise, this is a team game and having that extra gun could make all the difference in a team fight.