That is very easy buddy!
1. Backup your entire web-site root directory that contains all the files essential for the website correct functionality use FTP FileZilla or similar then upload them to your new hosting!
2. Log into your phpMyAdmin, click on the database and then on top of the screen click on the tab called "export" depending on your version complete the steps to download or backup your database! Once you have it downloaded go to your new hosting phpMyAdmin and this time click on the tab called "import" and again complete the steps to install your database!
Don't forget to connect your script to your database as I am sure the database name and password so it the host will be different!