I have experience with all the roles in the game and all champions, so it's not difficult for me to offer advice on any role or with any problem someone would come to me with.
League is a different game every single time you queue up to play, so there aren't rules set in stone that will always be available. Even ones like 'don't gank a losing lane' can be changed when that laner is full of crowd-controlling abilities and I can actually work something out with him.
So for a particular player, I have to see their playstyle first of all. This way I can see their strengths and weaknesses, so I know on what to focus and what to advise that they focus to improve as well.
In this manner, I coached someone that wanted to play a champion that purely relied on skill shots, while their playstyle was that of going ham. It purely didn't match, so, on my advice, we chose something more fitting.
To tailor coaching strategies, I need to know my students better. After a Live Game Session or VOD Analysis, I'm able to make a customized training plan based on the student's level and experience. Of course, the training plan will be a little bit different for Junglers and for example Toplaners. For me, the most important thing is to make a student aware player. Every role has a different role in a team and they need to know that.
When a player is OTP, usually he knows about his champion's strong and weak aspects. In this case, I pay more attention to his micro and macro mistakes. Also, I ask this type of student about matchups and power spikes, I just want to ensure he has proper knowledge about his main champion.
Observing the student is the key thing here. Analyzing the gameplay is one thing but also listening the the sentences and even the way the student says them is extremely important. Many people who book coaching are rather shy I've noticed and then you really have to dragg information out of them and break the ice to make them really comfortable so that they are willing to fully engage with me to give them the most possible value from our session for example.
However with someone who's more confident and dares to say more things I might have to try and tone them down a bit or give them a different approach. Coaching is as much people skills as it is gameplay and analyzing skills.
This has already been answered in the previous questions. To add up: team's objectives rarely exist in a soloq game. Player should focus on repetitive parts that can be improved upon (especially in the lower elo part of the community) and driving up to deliver the game as quickly as possible. Otherwise we run into numerous complications - longer the game goes. If one can understand, that soloq can be sensed as a single player game - where we cannot control 'our NPCs' (teammates we meet playing soloq) and he's able to progress himself in this whole story of grinding countless league games, the sooner he will start seeing results.
I usually just ask for champion pools and some informations that I gather when I'm naturally coaching them. You just have to be a detective, ask everything that you think it's needed to play a good game of league and then try to see if your students do the same as you or they have anything different that can distract them. This could be related to the game but also to personal side areas like friendship, love, having a bad day or simply not having the will to talk with a teammate because he hates him. A coach has to fix all of that and prepare his team till the end of the draft to make sure everything is on-line.
For the most part, the strategy that I work to impart most to students is a strategic, macro oriented style to approach the game. Usually I emphasize aspects of the game like rotations, wave control, reset timings, itemization, efficiency, drafting selection, team-fighting, game planning, and the mental side of the game. I don't tend to focus on mechanical or micro-oriented part of the game, such as trading, combo's, or team-fighting.
By observing. Different players has different ways of learning, just like studying in school. My strategies consist of trying to figure what training method suits my students the most through paying attention to what skills are they lacking ,directly asking them and a little bit of trial and error.
And I will swtich things up according to what suits my student the most.