To win games in competitive you're going to need to strategize and respond to your opponents strategies. This involves counter-picking, choosing a team composition, focusing heroes and choosing where your team sets up.
When forming your initial team composition factor the map, what heroes your team is comfortable on and what heroes the enemy team is comfortable on into your decision(if the enemy team has a Pharah main , you're going to need a hit-scan). Don't get to worked up about this as team composition isn't the be all and end all. We've got another article on how to encourage your team to form a decent composition.
You're also going to want to repick heroes throughout the game in order to counter the enemy team. The most common hero you'll find yourself needing to counter is Pharah. To counter her just pick a hit-scan such as Mccree, Soldier or Widowmaker, Zenyetta works well against her too. It's not just the hit-scans responsibility to deal with the Pharah though. If any enemy dps is carrying hard your whole team should be focusing them.
If you're on defence you have the opportunity to set up, so use it wisely, set up so your team is aiming at but not a choke-point, don't set up inside the choke point. This will make it tough for the enemy team to push through it.
It can help to base your team comp of off the current meta but it isn't the end of the world if you can't, as these team compositions are generally only necessary in the pro scene. The meta as I'm writing this is Dive Comp, so try to pick it if you can but if you can't don't worry about it. Just make do with what you have and try to encourage team-mates off troll-picks.
Another thing that'll be important to your Overwatch game is learning when and when not to attack the objective. If the objective is yours always contest it if you can, this wastes the enemy's time on 2cp and payload and gains your team some extra percentage points on king of the hill. If the enemy team has the objective never contest it unless you think you can take it, so generally when you're grouped up with your team.