Get in Position and Cooperate: Whenever you are in a team fight, keep all your squishy player to the back of the team and shield them with your tank, support and jungler from all incoming enemy attacks. To put this in perspective, your team has to cooperate like the parts of a killing machine (a military tank). The ADC and the Mage are usually the players with the most damage output, so they could be considered the weapons of your tank, while the rest of the team make up for the body that takes the incoming hits from the enemy artillery.
The better you position your team in League of Legends matches, the higher chances you get to win every team fight.
Keep your Creep Score healthy: Early game, or lane phasing, is the part where you have only one objective: FARM-FARM-FARM. If you manage to out-farm your opponent you can buy better items and become deadlier by the minute. The best way to farm is last-hitting and this takes time and practice. Remember, no one was born with this knowledge, so go practice as often as possible in PVE games.
If you get harassed too often and you can't farm, try to last hit minions at your tower. Melee minions take up 2 shots from the tower before they can get last-hitted, while mage minions must be hit once by you then once by the tower and ultimately last-hit from you. The bigger minions take more shots with less damage input, so keep an eye on them to ready your killing blow.
Manage to kill 100 minions every 10 minutes and the game is yours.
Always have Pink Wards: Force your team to have at least 1 pink ward before you go engage the Dragon or the Baron Nashor. Red trinket is useful but if the enemy team has more wards than you, there is a high chance they can steal your objectives right from under your nose. Placing one of this sweet babies will not only uncover all traps and other vision wards, but also stealth enemy champions that will try to sneak up behind you.
A pink ward costs only 100 gold and you can end up with so much more gold if you manage to use it wisely.
Ward in Jungle Fights: Never fight in an unwarded jungle. It can easily get a messy fight if you can't spot your enemy in the fog of war. Besides team positioning and coordination, force your team to ward every bush and area, in the jungle, before you even start a fight.
Be smarter than your enemy and all your foes shall parish like flies in the wind.
Wait for Inhibitors: If the enemy team managed to destroy one or more inhibitors, defend the base until they respawn or you defeat the oppressing team at your "gates". With an inhibitor down, the super-minions will push that particular lane like crazy. Preventing them to reach the nexus will prolong the game and give you a fighting chance to get back on your feet and destroy the enemy.
A dead inhibitor is a free invitation to all you can eat buffet in your house.