I highly suggest starting off with AI games. You will be matched with new players also trying to figure it out for the first time and no one will get mad at you for having no clue what is going on.
Try to play every champion in the free rotation each week at least once to begin building up your knowledge of the champions and what skills they have. When you are playing against them, you want to know what your enemies will be throwing at you, and the best way to learn that is by actually playing the champions to the point where you have memorized their 4 skills.
Other than that, the goals are fairly straight forward. In your lane, attempt to last-hit as many of the minions as possible from each wave. This is arguably the most important skill in the game that will determine how quickly you can rise in ability. As you get higher and higher in skill level, early kills become more and more rare, making minions the primary source of gold. Gold = items and items = damage. When trying to maximize damage, it is obvious why this is extremely important. Other than that, try not to die, and play focused on achieving objectives with your team. These start with killing towers, killing the dragon and baron located in the river running through the middle of the map, and breaking lanes (this is when you destroy the inhibitor inside an enemy base allowing you to spawn super minions in that lane).
The key to winning lanes is maximizing damage given and minimizing damage taken in trades (trading damage with the opponent in your lane) while maintaining a high level of minion kills.