Focus on one concept at a time. If he's willing, have him watch you play a few games and talk about what you're doing. This is a lane, that is a turret, these are minions, etc. Basic information at this point - no micro or macro gameplay ideas yet. This will hopfully help get him a basic idea of the map, what things are where, and generally where he should go and/or do. Encourage him to ask you questions if he doesn't understand what you are doing moment to moment.
Once he's made an account, go through the intro stuff. I'd say watch him do it so you can answer any questions he may have as they come up, but also do not tell him what to do or offer more information up at this time. Tell him buying thornmail on ashe is a bad idea though.
Then go into to co ops (think he's actually going to be locked out of other modes for a few levels) It might, again, be best to watch him play so you can answer questions, but it can also lead to being overbearing if you aren't able to passively watch and/or make small suggestions at a slow rate.
Start with the basics - these are minions, turrets, lanes, jungle, river. Don't attack the things in the jungle. Pick a lane (this champ usually goes this direction) and stick in it for the game. Kill things to get gold, use gold to buy items. Use recommended items for now, but take a look in the shop to see what there is if you want.
Once he's got that level of information comfortably assimilated, start on more advanced ideas like last hitting minions or prioritizing building an item completely rather than just buying what you can afford at the moment. You can also start talking a little about stats - AD, AP, ratios, armor, MR, etc to start introducing those ideas.
Of course, tailor the information to the specific champion he's playing - mage talk about ap, mr, etc more than ad for example. At this point, he should know enough to play around on his own. Also encourage him to read up on champs on the universe or in the client, just to get an idea of who is out there. I generally recommend new players try a mage, adc, melee bruiser, and tank, just to get the feel for the different styles of champ. Chances are, one or two of those will match his playstyle.
Once he's gotten a champ figured out, you can go a bit more detailed on position, role, build path, and combos/tricks for that specific champ. You can also start talking about some macro level ideas, like watching the minimap or grouping.
At this point he's hopefully going even or positive against intermediate bots. Throw him to the wolves and see how he does in a real game. Take time after each game to analyze it and talk over any issues, confusion, or questions he has about why things went the way they did. One thing to note - in normal games, a low level queued with a 30+ has a higher chance of being matched against low 20s, so you might want to make a smurf account just to play normals with him to keep the playing field as level as you can. If you do this, don't be a jerk to the other low levels.