Please tel me...

You can do a 1v1 by creating a custom game and inviting another person to your game.

Custom games can be started with any number of players, even if teams are uneven or unfilled.

1v1ing with friends is good practice, but I wouldn't take anyone seriously that says something like "1v1 me bro". They are generally butthurt after a loss, or getting called out. While some champions excel at dueling (fiora, xin, jayce, etc) it's a team game, and fighting them 1v1 comes down to more which champion is picked as apposed to skill.