The very first thing that you have to learn is the game that you are playing, no matter if it's a FPS, Moba, MMO... every game requires his time to be mastered, having some old experiences can surely speed this up.
Aim for FPS
The very first thing that you have to learn when you start to play a FPS is to aim, yes because aiming is the core of the game, the faster and better you aim, most likley you will kill the enemies and if you kill the enemis you win the game.
There is not really much to say about this, you improve mostly with time and constancy (read mind and muscle for more details), but how can you improve faster? you will find the answer if you read this "guide" till the end.
Positioning yourself in the right place in the map is really important and very often key to win games, if you play moba/overwatch, tanks have to stay in front of the team and are the first to engage, dps in the mid and healer behind the team, exception made for assassins/flankers who can go in, kill and get out without problems.
Your role, your job:
Tank: Help dps to do damage but mainly defend your healer if they need help
DPS: Do damage without overextending or going out of position too much and if someone is disturbing your healer focus him.
Healer: Heal who needs, but don't stay to far away from the rest of the team, or you will be an easy target for flankers
In Overwatch the highground is very powerful, abuse it.
Learning good flashbangs/smoke spots is very important as most of the game goes around this, specially when playing with a clan.
If in a game you are having bad time in getting kills and you're always going to the same spot in A, try to swap position with the one defending B this may work. On the terrorist side you are most of the time likely to go all together, always flashbang before going in!
Don't be too greedy
Most of the time if you play too aggressively and that means overextending, going away from your teammates just to confirm a kill may be good sometimes, but what if you can't finish him off? if the enemy runs back to his team getting so heals and protection, you will surely die at this point and end up to leave your team with one less forcing them to fall back and lose points/turrets.
My advice is to avoid to overextend if you're not sure that you can kill him and get back safely, only in moba if someone is extremely feeded you can take the risk to finish him off and overextend.
Teamplay and Duo
Useless to say that teamplay is really important because on high levels you will find hard time to carry games alone, you have to rely on each team member, if it happens that in your team you have an inexperienced player who goes alone and don't follow the team or does some mistakes, try always to stay calm, most of the time if you're nice with the subject he will try to improve his gameplay and follow what you say, otherwise if you lose your head the team will lose another member, because you lose concentration and start to discourage yourself, even if your teammate don't follow what you say, try to win the game anyway if you fail you have to be conscious that you playied your best.
If you have a friend who has similar or even better skill than you try to play together, if he is better than you, you can learn alot from him and you can play and comunicate with someone that you know, increasing your chances of success.
If instead you understand that in your losing streak the problem is your friend you may consider the option to play with him using a smurf or just some casual games, thats may sound malefic from you, but you have to improve and going up with your rank.
Most of the game now have a voice chat, making it easier to comunicate with your team, for the games that don't have the voice chat there is always the text chat.
Why is comunication so important? simply because having information on the battlefield will help you making better decision and