Step 1: Have a lane in mind BEFORE you pick a character
As you play, you will quickly learn each character's preferred placement on your team. Look at the characters your team has already chosen and do your best to fill in the gaps. Eventually, you will begin to catch on to advanced concepts like team composition and "The Meta", but until then, choose characters you feel comfortable with and experiment. Your team composition doesn't matter when nobody knows how to play (yet).
Step 2: Have your priorities in order
Through the laning phase, your priorities (from most to least important) are:
-Destroy the enemy's tower
-Gain XP (be in range when enemy minions die)
-Last-hit enemy minions for gold
-Deny the enemy XP and gold by zoning
-Harass/kill enemy champions
Note that the order of these can change depending on the circumstances; for instance, you may decide it's more important to keep the enemy from farming so as to delay their build. However, not dying is always the most important. When you die, not only do you give the enemy gold, you are missing out on XP/gold by waiting to respawn and walk back to lane.
Step 3: Control your zone
First, watch Shurelia's zoning tutorial: http://www.youtube.com/watch?v=0kxGQ3gWdrM
Each champion has an area around them that they control, the size of which depends on the ranges of their auto-attack and abilities. Avoid walking into enemy zones and use yours to create pressure. If two opposing players walk into each other's zone, they will trade damage, and whoever deals more will come out ahead. Learning the size of each character's zone and the damage available to them in lane comes with experience.
Pay attention to how minions and brush affect your zones. Minions block most skill shots, so don't hesitate to use them as a shield. Enemies need sight of you to auto-attack, so hiding in the brush can foil those pesky ranged carries.
Step 4: Understand aggro
"Aggro" is when the AI controlling the enemy's units focuses on you. You don't want it! All minions, towers, and enemy champions targeting you will have a yellow border around them.
-If you attack an enemy champion, nearby enemy minions will aggro you. At the first few levels, they will deal significant damage to you.
-Towers aggro the first enemy unit to walk in their range, so let minions go first.
-If you attack an enemy champion under their turret, they will switch aggro to you. Be careful!
As you get more experienced with your character, you may choose to "tower-dive" (ignore aggro) in order to kill a low enemy champion. It's a risky move at all levels of play.
Step 5: The art of the last-hit
Learning how to last-hit is the most important skill you can learn. In terms of resources, LoL is a race to farm as quickly as possible and buy your end-game items. The more gold your team has, the stronger you are and the larger your advantage over your opponents. And while champion kills are worth a lot more than minions, keep in mind that about
So how do you do it? Simple: get the last hit on as many minions as you can. Watch the minions' health bars and find which ones are decreasing fastest. When they have only a sliver of health left, right-click them. Success is dependent on good judgement and familiarity with your character's damage and attack animation. Don't get discouraged if you're having trouble; remember, it just takes practice!
If the minions have been pushed back under your tower, last-hitting will be more difficult. You may need to use some of your abilities to keep your tower from stealing the gold. Again, practice! Some tips:
-Melee minions will be left in last-hit territory after two (2) tower hits. Let the tower hit them twice, then finish them off.
-Caster minions are trickier. Try to hit each one once BEFORE they get in tower range. One tower shot at this point leaves them in last-hit range.
-If you issue a "hold" command (bound to "S" by default), your champion will not auto-attack the creeps until you issue a new order. You can use this to time your last-hits easier.
Step 6: Don't push your lane!
At the beginning of the game, each team's first minion wave will clash right in the center of the lane. As you fight, they will be "pushed" towards one side or the other. In general, you want to avoid as much as possible situations in which the wave is on the enemy's side of the river. Why?
-You will be further from your tower. That is, safety is that much farther away should something go wrong.
-The enemy will be closer to their tower, and therefore harder to finish off.
-You leave yourself open to ganks from other lanes or the enemy jungler.
The ideal place for the minions to clash, then, is on your side of the river. This forces the enemy to stay on your side of the map, making them more vulnerable. Since dealing damage to enemy minions pushes the lane, the Golden Rule of Laning is:
Last-hit, and ONLY last-hit!
Of course, when you have a good opportunity to damage the enemy tower, you need to push the lane first. If you do it fast enough, the tower will even kill off all your minions and "reset" the lane back to the middle. An aggressive lane may also choose to push the lane to put more pressure on the enemy.
Step 7: Wards are NOT optional!
Sight Wards, available in the shop for a mere 75 gold, are your best friends. You may not realize it, but the lowly ward is the most important item in the game. Why? Because LoL is fundamentally a game of area control. By gaining more sight of the map, you gain direct influence over the game. In short, Map vision enables good plays.
In the laning phase, wards are important mostly because they stop ganks. When you place a ward in the river brush, you are making it safe to push your lane. If you see someone coming from the river to stop you, book it. Without that one measly 75g ward, you would probably have died, giving at least 300g to the enemy and missing out on way more than the 75g it would've cost you. So don't forget!
-If you have more than 75g left over after buying items, buy AT LEAST one (1) Sight Ward.
-It is EVERYONE'S responsibility to ward the map as much as possible.
-If you don't see your lane opponent for awhile, it is considered good etiquette to call "MIA". However, it is YOUR responsibility to watch the minimap for missing opponents. Consider MIAs a luxury.
(For those of you wondering, Vision Wards are used to watch for stealthed champs and enemy wards. You generally don't need to bother with them.)
So, that's pretty much everything! It's a lot to take in, to be sure, but it's all important to a successful laning phase. And since the laning phase decides the shape of everything that comes after it, you owe it to yourself to do your very best.
Win the lane -> win the game!
If I've forgotten anything, I'm sure someone in the comments will help me remember. :)