The tutorial match which comes up after the basic tutorial gives you a bit less than 500 IP, enough to buy a cheap champion and runes to fill out your available slots. You don’t have to buy a champion though. I recommend only buying those you already played when they were on rotation and actually liked.
Play all of the champions in a given rotation at least once to familiarize yourself with their abilities and play, it will help you make better decisions during the match. Note in particular which champions have crowd control abilities as they can put you in a very nasty position very quickly.
For runes, I wouldn’t bother with tier 2 and just stick to the cheap tier 1 until you reach level 20, when you can start buying tier 3 runes. You will have more IP to spend on the more expensive champions in the long run. Runes are not a big deal in the early levels, just make sure you fill them up.
Here is a guide to help you make decisions once you get to tier 3.
Do not play on intermediate difficulty early on though. The AI gets more gold apparently and it is possible to lose easily if you’re not careful. Beginner, however, is very very easy.
As for actual play:
The default lane distribution is 2-1-2. Two players top, one in the middle, two at the bottom. In early normal games you will see several people going one lane and leaving one unattended, things like that. Try to nudge them in the right direction a bit. Stick to your tower before minions spawn. At most, go into the closer grass if you’re at top or bottom lane, but only if you can get there immediately. Lower level players have this unending desire to gank you from the grass closer to you tower at level one, so watch our for that.
Later on you will see junglers, which means someone who instead of farming in lanes kills creeps in the areas in between, called the jungle. This usually means your distribution will be 1-1-2, leaving more creep kills for the top lane unless the enemy team does not have a jungler of their own, in which case top lane will be playing more conservatively.
Look for smite on the loading screen to spot junglers, and be wary when they come out of the long grass ready to kill you. They will have picked up buffs from stronger creeps in the jungle, of which there are two on either team’s side, and be quite a threat if you’re not careful. In the long run you will need to guess when to expect a gank by a jungler depending on his route.
Learn to last hit minions. This is an important skill to learn. Experienced players do not autoattack enemy minions in the laning phase, but wait until allied minions reduced their health enough that a single hit from you kills them, giving them a small amount of gold for the kill. You will have to learn how low the enemy health bars can go before you need to move in and start your attack animation. If your lane goes badly and enemies prevent you from getting last hits, try to at least stay in range to get experience and wait for the minions to get pushed back to your tower, where you can farm safely.
This is another reason why you only last hit minions. If you autoattack and use abilities, your minion wave will get pushed to the enemy tower, exposing you to ganks from the river and making it hard for you to last hit properly.
Play conservatively. Do not tower dive, that is running into range of an enemy tower to kill a champion until you are high enough level and know you can get away with it.
Do not face-check bushes, that is walking into the long grass when you don’t know where your enemies are unless you are a tank with your team nearby or you’re sure you can get away with it.
If you have low health and get away from a fight and an ally is still engaging the enemy, do not run back to get an ability or two off unless you are sure you can get away with it.
There is a pattern here. Knowing what you can get away with is what separates good players from bad ones. Until you learn this, just try to stay back a bit, even when your teammates scream at you.
solomid.net is a good site if you’re looking for guides for particular champions. Make sure the guide you read is both current and approved to be on the safe side.
Finally, don’t get discouraged by shit-talking, and have fun with the game.