How do you send a personal message to someone in League of Legends?
Solution 1:
In game you can type: /w "[player name]" [message]or /msg "[player name]" [message]. After they've messaged you once, you can just type: /r [message] and it'll go to whoever messaged you last.
In lobby/champion select, you can double click on their name to bring up a chat.
Note: this only works with the ones in your friends list.
Solution 2:
You can also type /msg instead of /w They do need to be in your friends list however, so you can't harass people or stalk players, which is a good thing. :)