1.) The players gaining the most gold in the beginning of the game often have the most influence on the outcome of the game later on. It's very important you ALWAYS try for the last hit on minions since you only gain gold from placing the killing strike.
2.) Stay behind your minions until you reach level 4. Harassing your enemy early on is an effective way of limiting the gold/experience they accumulate, but if you're taking heavy damage from enemy minions while doing this harassing, then you're essentially making it easier for the enemy champion to gain gold/experience 30 seconds later as you will be forced to return to base to heal.
3.) If an enemy champion disappears from your lane, let the rest of your team know so they can prepare for a gank. This is accomplished by simply typing "mia" into chat. (Specifically, if you're in the bottom lane and an enemy champion starts to head to the middle lane, type "bot mia" in chat to warn your ally in the middle lane that an attack is imminent)
4.) Buy runes & gear that compliment your champion's passive ability. For example, Blitzcrank essentially gains hit points from items that contain mana-boosts; Tryndamere gets more critical-strike chance based on how much of his life is missing, so it doesn't make sense to buy a vampiric scepter for lifesteal in the beginning of the game as this will directly conflict with Tryndamere's ability to strike critically on enemy minions/champions.
5.) Play your champion based on the type of champion he/she is. Ashe, for example, is a hard-hitting ranged striker with very little health and armor. A successful Ashe will keep the enemy at a distance at all times and will not try to "tank" the enemy.
6.) When in a team fight situation, always try to initiate the enemy champions with the least amount of health, or the enemy that hits the hardest. (Usually if the champion does a lot of damage, they don't have much health/armor) Avoid aiming for tanks such as Shen, Alistar, Rammus, Malphite, or Amumu until the other enemy champions have been slain.
7.) Backdooring towers/inhibitors is a great way to catch the enemy off guard and suppress a focused enemy attack. Champions such as Master Yi, Pantheon, Tryndamere, Twisted Fate, and Teemo can break away from the group and push lanes relatively quickly with the ability to escape unharmed as they are very tough champions to catch on the run.
8.) Place sight wards in key areas of the map. Placing sight wards is a great way to setup ambushes, keep an eye on neutral-buff characters, and foil enemy ganks. For best results in a 5v5 match: place a sight ward in front of the Dragon, Baron Nashor, and in various bushes in the jungle. For best results in a 3v3 match: place a sight ward in front of the Dragon and directly behind the Lizard Elder.
9.) Spend your gold when you return to base. Gold is used to buy items to help your character dish out damage and stay alive, so spend it! You may not be back to heal for several minutes... several minutes where your gold won't be working for you. As a rule of thumb, never leave your base with more than 1850 gold.
10.) Kill the Dragon and Lizard Elder whenever you have control of the map. (You have map control when the majority of enemy champions are visible and busy defending their towers.) Killing these neutral-buff characters yields gold for your entire team, extra bonuses such as damage-increases or an attack that slows your enemy, and experience.