The answer to this question could be very long and complicated as "leading" involves keeping track of a great many thing all of which are detailed in themselves. Lets start with the basics each of which can be expanded and may be scenario specific.
Firstly, since you are asking the question we are going to assume YOU are going to be the team leader. As such, you need the following skills.
- Champion Knowledge
- Allied Champions
- Enemy Champions
- Map Awareness
So Now lets break this down a little further
You need to be able to guide your allies to accomplish whatever objective is in the best interest of the team and you need them to listen to you. Therefore, you should probably be talking and communicating with your team from the start of the game. If you start to bark out orders once everyone is level 9 or at the 20 minute mark, no one is going to listen to you because they will have developed their own strategy since none was presented to them. This being said, commanding and just pinging are insufficient to obtain the role of team leader. Some players will respond to "mid needs help" while others will need to be explicitly told and yet others won't ever listen to you at all (it happens). So you need to know the players on your team almost as well as the game itself to be an effective leader.
Champion Knowledge - Allied Champions
You have to know the capabilities of the champions you are leading . Note the emphasis on the preceeding "." You have to know each of your ally's strengths, weakness and limitations. Ideally you should be familiar with all of their abilities and those ability's strengths, weaknesses and limitations. There are too many champions and abilities to cover them and their interactions here but here is an example:
Let's pretend your ally is Jax or Katarina and they are in trouble. Sometimes, you can save them by being in range of their Leap Strike/Shunpo abilities, allowing them to jump out of a gank. Leading is often more about being in the right place at the right time than telling other people where to be. If you are often at the right place at the right time (leading by example) players will recognize your competence and tend to congregate where you are, which is nice when starting a group push is your intention.
Champion Knowledge - Enemy Champions
Knowing your team is important but knowing the enemy team might just be more important. Knowing enemy champions, abilities and tendencies will allow you to make the correct decisions regarding: who and when to gank, when and where to push, watch to watch for when being baited, etc. Note there are guides to all of the above elsewhere so a detailed description of each will not be covered here. However, here is another example:
You are chasing an enemy at low health but there is a Teemo on the enemy team. Odds are the champion you are chasing will lead you on a trail through Teemo's mushrooms in hope that they will slow you enough that they get away or kill you if you are at low health. As the leader on your team it is your goal to remind your allies of this and minimize losses through overextension.
All of the above is worth nothing if you aren't aware of what is going on in your game. What lanes are being pushed? What allies are in distress and in need of assistance? Where are enemy champions? Is the Dragon minion available to kill? Is the enemy team currently killing Baron?
You have to be playing your champion and simultaneously aware in some way of all of the above. Things like the Mini Map and communication are good tools to make sure you and your allies are aware of what is going on but there is also some degree of awareness that comes with experience.
This answer was intended to focus more on the act of leading than to describing the specific situations and circumstances which may be encountered. In the end, every game situation is unique and will need a different approach. It should also be noted that mastering the game mechanics and becoming a good individual player is not the same as being a good leader. Communication and team play are imperative when seeking wins and an improved gaming experience overall.