Here is 10 different starter tips for the game League of Legends.
1) League of Legends is a TEAM game. I'll say that again...League of Legends is a TEAM game. Don't try to be a hero when you are just starting. If you try to do too much as a beginner, you will end up being the reason your team loses the game.
2) Do NOT Die. I cannot stress this enough. Most players come from games like World of Warcraft, or real time strategy games, where losing a a single unit isn't really a big deal. While it may not seem like a huge issue to be dead for 30 seconds, it usually means your enemy players will gain a level or two and 100-200g that you did not get, and it only gets worse as the game goes on and the death timer is increased. Also, while the experience rules have been changed recently to prevent things from snowballing, it can still happen. If you give a good fighter or mage character 3 or more early kills, it is going to take at least 3 of you to take him down, and that's if he's alone. Overpursuit is probably the most common type of death, but is easily avoided, and will get your teammates frustrated very quickly.
3) Attacking a champion causes everything computer controlled in range to attack you. This includes minions and towers. As a new player, hitting an enemy champion anywhere near a tower should be completely avoided until you know what your limits are.
4) You do get a constant stream of gold, but your main source of income is killing minions and champions. You receive gold for getting the killing blow on any minion, or for getting a champion kill or assist. Your entire team gets gold if a tower is destroyed (100g) or if anyone kills the dragon minion (165g). It's very important to not be passive in a lane, you should be trying to kill minions as much as possible.
5) Call missing in action (MIA) champions. For the first 15 minutes or roughly 10 levels of the game, and at lower summoner levels and ELOs, players tend to stick to thier lane while they build up skills and gold to help in the end game. Laning can often leave players in vulnerable positions. It is your duty to inform your team mates when someone is not in your lane so they know to be on thier guard. A simple 'top mia' is sufficient, naming the champion is better ('annie missing top') as it helps others know what to expect. The best thing to do is to combine the this with pinging the map (alt clicking on the mini map is the fast way) a few times in the general direction the player went.
6) Pay attention to the map. At a minimum of every 15 seconds (I personally am closer to 5), you should take a glimpse at the map and see where all of the enemy champions are. If you are in a vulnerable location (more on that in a second), and none of the enemies are showing on the map, odds are they are coming for you and you should head to safety immediately. If you can see all multiple champions harassing an adjacent lane, you should be ready to come and help your teammates. If your teammates have the entire enemy team occupied at a tower on the far side of the map, you should be pushing toward the enemies base for as long as it is safe to do so.
7) Don't be a laning robot. One of the biggest mistakes I see from beginning players is that they fall into laning and pay attention to nothing else. If you die, the first thing you should do when you respawn (or even while you are dead) is look at the map. Starting as soon as level 10 (although usually more around 12), you should very rarely be alone, and most of the killing and tower pushing will be done with most or all of the team together in one place. If your lane has minions pushed all the way to the other side of the map, and the enemy is near your base in the opposite lane, don't feel compelled to stay in the same place.
8) Know your escape route. If you are alone, or with just one other teammate later in the game, always be aware of how far you are from the nearest safe spot (tower or your base). If you have a short escape route, you can be a little more agressive. As the game progresses, you should be VERY cautious about being on the enemies side of the map alone, because escape will be virtually impossible if you run into more then one champion.
9) Support your teammates. I've put a lot of stress on not dying, but it's important to not be a coward when your teammates are involved. If you have a fight that is anywhere near close, it is better to die fighting with your teammate then to let them die unopposed. If your lane partner is being attacked by enemy champions, you need to put the pressure on them as much as possible. Remember, the team that dies the least is usually the winner, so it is just as important to make sure that none of your teammates die if you can do anything to avoid it.
10) Play every champion at least once. It's the best and fastest way to understand what thier capabilites are, and what tactics opposing players will be using to try to kill you. I have seen countless deaths as a result of a player not knowing what the champion they are fighting is capable of. For example, Rammus has an ability that forces you to attack him for a few seconds. He ABSOLUTELY must be early game when he is near a friendly tower, or when he taunts you, you will be attacked by the tower and surely die. Even if it's only practice games against bot opponents, you should try to play every champion right away, even if it's only once.
11) Don't take the game too seriously, have fun. It can be very tough as a beginner in League of Legends because it is very easy to be the reason your team loses the game, and people are quick to vent thier anger. Since normal games are the only avenue for matched play right now, the pool includes people of all experience, skill, and dedication levels. That means often there will be people who are hardcore and only care about winning on your team. Don't sweat it. Riot is working on ranked games, and when that comes in, it will be a much better environment for beginners. Just try to be an attentive teammate, have fun, and the rest will come!