One serious way to do this is to look at the actions and methods of players who do well and the actions that you take (usually means learning new skills along the way) and compare them while also looking at the situation. Then apply this knowledge to games and find out for yourself, which method works best for each situation and what methods are most effective to you.
These are the things i tend to passively do because I'm interested in that sort of thing but I'm not into improving my skills because i play for fun (thus i avoid ranked like the plague). But I have noticed that over time my skills have gotten better (without realising it unless i specifically check for it).
The other way like advertised by Riot themselves is to do progressive drills for what you feel is your greatest shortcoming (intermediate bots are best for this - use champs like brand because they can punish mistakes unlike others which are rather useless). Typically you can improve your whole gaming prowess by improving a single fundamental. For example Boosting reaction time and awareness through minion farming / last hitting affects how you play as a whole and could be helpful.
Sorry about the mostly useless monologue (i could have just bullet pointed it really).
Oh also you should definitely consider Zerg's approach too it's a nice way to develop quick thinking.
