While I can't fathom how normal people find a game this hard fun, I can simply accept it. That makes it quite possible to get our friends and significant others hooked. However, because League is a hard game, it is probably best that we be careful when we try to teach our friends. It's pretty easy to scare them with the enormous difficulty in the game.
The biggest thing you want to avoid is explaining laning mechanics. Optimal play isn't obvious! Trying to explain why lane pushing is bad causes people's heads to explode. Just note that scoring the last hit nets you gold and stop there. As your friends improve, they'll ask how you get so much more CS than they do, and you can teach there. If they don't ask, you shouldn't explain it.
Instead, focus on things that cut through complexity. Item and skill orders are the easiest things to do in that regard. The item system is a huge block of complexity that confuses new players, even with the recommended items list. Pick items out that will be most helpful and explain some of the other choices. I went a long way in my career only knowing to buy Phantom Dancer/Infinity Edge/Bloodthirster on ADCs. Now there are more choices like Statikk Shiv, Blade of the Ruined King, and Mercurial Scimitar. It can be incredibly tough to navigate those options without guidance, so that is where you can be most helpful.
There are roles like jungling that are fairly complex to understand for newcomers. It should be explained in fairly easy terms (more total exp and gold for everyone). If you smurf with lowbie friends, you probably shouldn't play a normal jungler. I find that under level 30, teams almost never have junglers. After level 30, they are fairly common (due to featured matches, pro streams and such), but the majority of junglers below 1300 elo are completely awful. One could argue that the majority of players below any given skill level are bad, but since jungling requires much more game awareness than other roles, they tend to be worse than the average until one gets into the top 10-15% of players.
If you know some things about a matchup, it can be good to give some quick, small pointers on the matchup before the game starts. If your friend is Ryze against Syndra, it might be a good idea to let him know she can push her balls at him to stun him and throw minions (both his and hers!) at him. Don't give a lecture on how to play; just give little advice points.
If you link your friends to guides in the infant stages of their League careers, they had better be pro guides to characters like Master Yi, Karthus, or Anivia. Try to avoid "boring" guides like mine or those on more "tryhard" websites like LoLPro until your friends are actively seeking out knowledge.
Playing League can be pretty frustrating for a beginner, especially with an expert tagging along. There are few ways to show how bad you're performing better than having someone else dominating to compare yourself to. If you're asked, provide little bits of information slowly.
My first experience playing LoL with my girlfriend was pretty jarring for me. She wasn't bad for a beginner, but I played on my smurf account as a free week Vayne and got to see first-hand just how much worse low-level players were (my smurf was around level 5; my girlfriend was a little under level 10). She did fairly well for being a beginner, but I dominated the enemy team so hard that it didn't really matter what anyone else on my team did. Afterwards, my girlfriend lamented that she sucked, which of course wasn't really true. Compared to someone who had played the game for a year (at that time, anyway), she was definitely weaker, but she was using the skills and knowledge she had as best she could. One does not learn stutter-step micro in a day -- unless you learned it from another game first.
It can be frustrating when your friends cannot do something as simple as "Just click on him with skills! OMG!" Try not to rage like I do when this happens. Their failings are steps on the road, and there's no shortcuts to improvement. The subtle things like when to attack and back off, when to push, when to go for a gank, when to vary your item build -- those are things you can't teach. I know this better than most. The most you can do is help them click on stuff better. In my case, even when I have a captive audience who wants to read about the game, the best I can do is show you that a skill exists. It's up to you guys to actually develop it. For people who just want to play to have fun, there's no easy way to teach. Just give little pointers and hope for the best.
We understand what it's like to climb the skill ladder in League of Legends. The Summoner's Guidebook teaches you the tools you need to get a competitive edge. Whether you're climbing the ranked ladder, playing Draft Dominion, or getting crushed by intermediate bots, every enemy has a weakness. And every Thursday, Patrick Mackey shows how you can improve improve on yours.