Keep in mind that the game's tutorial doesn't tell you about pretty much ANY of the important shit you need to know, such as:

CSing (last hitting minions and monsters)
Roles (i.e. tanks, attack damage (physicial)/ability power (magic) carries, mage-type supports, tanky initiating supports, etc.)
Jungle buffs and obvjectives
How to pick the appropriate champ in Champ Select
Proper use of wards
the list goes on

One great resource of information (and probably where you should have made this post) is over at /r/SummonerSchool. There are tons of guides and Q&As covering basically every topic in the game.

Nobody here is exaggerating when they say LoL has a steep learning curve. Some things you should look into after you have at least a very basic understanding of the core mechanics, other than what I mentioned above, include:

CS'ing (including freezing the lane/how many of each minions spawn and their exact worth/jungle timers and paths/minion aggro, etc.)
Choosing a champion thats right for your playstyle
Team compositions and pros and cons of each
counter picking in champ select
Item builds (dependant not only on champion but also role and countering)
animation cancelling (dependant on champion)
summoner spell usage
how the ranked system works
basic runes every summoner should have
how to effectively choose runes and masteries for your playstyle/champ/role
I'm sure there's more topics I missed

Some sources to get you started:
www.reddit.com/r/summonerschool
www.reddit.com/r/LeagueOfLegends (official LoL subreddit)
www.reddit.com/r/League_Of_Legends_
www.leagueoflegends.wikia.com
www.surrenderat20.net
www.solomid.net
www.learntheleague.com
www.skill-capped.com
www.champion.gg
www.pickban.com
www.probuilds.net

Hope this helped! -#SwainSwag

NOTE - I will come back in a little while and update this post with descriptions to the links I posted.