Play Summoner's Rift (normal or ranked) at least 1 game each day (you can make breaks between days, but it will slow down progress)
Play for 15 days and you will get 1 checkpoint or level up if you are already at 3 checkpoints
For rotating game modes it takes 18 days, for other maps did not try.
If you are penalized and now you are honor level 0 or 1 you will be locked for 14 days before you can start you progress.
Giving honors and getting honors does not speed the progress.
More games does not speed up progress.
Only the days you played on will count toward 15 days.
Reports from other players who reported you may slow down your progress ( each game reported 1 day more to play) but i am not 100% sure for that.
Statements 1. and 2. are 99% true, I actually tried it.
