Hi I am not the best player EU but I will tell you some mistakes I see people doing often (i am currently alternating between rank 1 and 2, ~3k MMR). The guide should be helpful for rank 10-50.

When an objective spawns (for example tribute), do not just take it. Watch the mini map. where is your team? Where is the enemy team? Are you ahead on lvl? do they have lvl 10 already?
What I see a lot on lower ranks is someone going solo to tribute trying to take it. 2 or 3 enemies jump out of the bush and kill him. when he is dead he watches the mini map and notices his mates are still farming bot.
Check the mini map. If you dont see any enemy but one of your mates is still bot, the chance is high you will fight 4v5. Just give them the tribute, don't fight when you can predict the enemy will win. If you see one of the enemies is bot and you are full 5 then go for it. When the temple spawns bot and you are already bot wait for your team! don't go there alone. be patient. let the the enemy get the first 5 shots and when your team is there go for it. If you are behind in talents (if they have lvl 4,7,10,13,16 or 20 and you dont have) or one of your mates is dead you can't contest it at all. just leave it to enemies and farm some exp.

Make sure every lane is coverd! The exp is essential in early game (well actually whole game).
if you are on a solo lane, don't go gank and leave your lane empty (An advanced strategy is to clear a wave fast and then go gank. But i don't recommand this if you are not 100% confident to not miss any minions exp). If you get the kill it just equalized the exp you lost on lane. if you dont get the kill you are behind. don't leave lane emtpy for mercenarys. you have 5 people. 3 can farm each lane and 2 do mercs. if you are 2 bottom and your solo mid dies go to mid until he is back. unless the objectives spawn all 3 lanes should be coverd. watch a random replay, only pay attention to minimap and if all lanes are coverd. you will be surprised. the main rule is farm to lvl 10. but if all buildings still up you can farm to ~lvl 13. if you start walk as team to early the enemy can easily destroy your walls and towers on empty lanes.

if you die at tribute because you tried to capture it 1vs3, don't blame your mates for not coming. instead tell them to come before you die. if you read the mini map you can know where the 5 enemies are. If one of your mates go there and die don't blame him because it was obvious. instead ping him to retreat before he dies. tell them to wait for the team and not to engage 4v5.

that is the most important one! maybe you noticed the other points required mini map already. The mini map is a strong tool of information. when you are dead watch it and analyse enemy movement. when you are walking from A to B watch it. When you go heal at fountain you can shift-click to go back to lane automatically and during the time watch the map. go watch a replay and click on a character of your team and hold down v (-Vision). watch the replay and only pay attention to mini map. try to predict where the enemy will go. release v and see if you were correct. try the same thing during the game. you don't need perfect mechanics to climb ranks but a good read of mini map.

No objectives are on the map and only a single yellow mercenary camp is left on the mini map. you will have the urge to capture it. but the enemy will have the same urge. this is kinda similiar to tip 1 (analyse the situation). could the enemy come to the camp? if yes could you fight them? if no, dont take the camp. wait for your team. you killed 3 enemies on botlane on black hearts bay. they are dead for 25 seconds. perfect time to take the boss right? you will need ~ 20 seconds to go top. and additional 20 seconds to kill it. the enemy spawn 5 sec after you started it and they have shorter way. propably they will just arrive when the boss is almost done and you are still low life, oom and your spells are on cd. you will die and enemy get the boss. if they dont see anyone of you on the lanes its obivous you are at boss. if you see 2 of them are defending bruiser on botlane and all 5 of your team are near boss you can go for it. the other 2 will need about 20 seconds + ~7 seconds they realize you do the boss. enoguh time to kill the boss. if the other 3 come, kill them and then take boss. ( you should win 3v5, even if you wasted basic abilities on boss).
Every time you take a mercenary and you die and enemys get it because your team didn't come it is your fault not your teams fault. Just leave it when you notice your team doesn't come.
before taking any camp ask yourself: is it safe? could the enemy come or are they dead/ need to defend something. if they come, who will win the fight?

All the tips seem kinda obvious and you knew it already? That is a psychologic phenomen I guess. Maybe you watch the mini map sometimes and know where enemies are at the moment. Your team didn't see it and you feel like they are all noobs. The thing is, you do it only sometimes. When a mate or enemy died, but you were not involved you should still immediately be able to tell who killed him and where he died if you watch the mini map carefully. Sometimes someone die and I am surprised. Huh? We kill someone? nice! And sometimes I take unfavorable figths because I think we are 5 but we are not. (happens when I forget a team mate is dead and I see no one hanging around somewhere so I assume all are here). But that happens rarly to me and that is what I need to improve. Even though you maybe know all those stuff your first step to improve is admit you don't do it permanently. I see even rank 1 players mess up that stuff sometimes so I am sure you mess up too some times.

I can understand if you want to play rather than watch boring replays but it can show off a lot mistakes you do! When you see others playing you sometimes think 'wtf are they doing' but you know what you are doing. Watch a replay of a game you don't remember anymore and you will see yourself like a foreign guy and think 'wtf am I doing?'. Also it's good to practice reading minimap. Go to the edge of map with camera so you can only focus on the mini map. Pay attention to the points above. Is every lane coverd? Try to predict enemy movment by only seeing one teams vision (holding down v-button). When it comes to a fight try to predict who will win (lvl 10 vs9? 3v4?). could the loser avoid the fight? Is it safe to take camps that they are just taking?

After you reached lvl 13 and some walls and towers are down you should start working as a team (there is no rule, usually you just feel when the team phase starts). If your team goes for the boss but you know it would be better to push, jsut go with the team. if you do the wrong thing as 5 is better than do the right thing alone. You win the fights easily if you outnumber the enemy. So always go with the largest groups of mates. (some exceptions when you split for mercs or something

- Don't fight if you will lose (even for objectives)
- Farm exp on all lanes.
- Don't take risky mercenaries just because they are there.
- Admit you do mistakes, not only your team
- try to figure out the mistakes by watching replays
- practice the read of mini map

If you die it is basically never your teams fault (when you die in a fair team fight it is no ones fault. that just happens). You lose the fight because 2 of your mates didn't come? Why the hell you fight then? 3v5 is not going to work! Of course it would be better if they came. But they didn't so don't fight. If your other mate engages the 3v5 let him die. Better 1 dies than 3. After losing a fight (even 3v5) they will all cry about bad focus. If you lose a standard 5v5 it still can be because positioning, someone had cd on ultimate, lvl advantage etc.. But in the lower ranks the games are not won by the team who do better in 5v5 because people keep figting uneven fights.