League of Legends has spread to all corners of the globe (minus Africa). If you wish to play on another server to experience the various metas, players, and methods of play, or if you are moving to a different country, there are only 2 methods of changing the server you play on : creating a new account or transferring via the client, which costs around $20. This guide will focus on creating a new account as it is free and easier.
Step 1: Visit https://signup.na.leagueoflegends.com/en/signup/index
Step 2: On the top right side of the website, select the region you want to play in.
Step 3: Fill in the details such as email, username, password, date of birth, etc.
Step 4: After setting up your account, download the client, and you're good to go.