Your website can be transferred to another hosting only if your current hosting and new hosting use cPanel. To start transferring your website, go to your current hosting account and access its cPanel. Click File Manager.
Proceed to the website folder which is located in the public_html folder. Select the folder and Compress it.
Click Download to save this zip file to your computer. As soon as the download process is completed, log in to your new hosting cPanel. Add your domain name to your new hosting in Add domain section. This way you will create a folder with your website name on your new hosting. Through File Manager upload the zip file to the new hosting → the public_html folder or to the folder which has been created earlier. Unzip your files using the Extract button to the exact destination folder. Once you have successfully transferred the files to the new hosting, you can start transferring your database.
Go to cPanel of your old hosting and choose phpMyAdmin in Databases.
Having connected to the database-management system, you will see all your databases. In the left-hand sidebar select the database you need to transfer and click Export. Export the chosen database in the SQL format and save it to you computer.
Access your new hosting cPanel → MySQL Database Wizard to create a new user and a database. Save your username and pass as you will need them later in the transfer process.
Proceed to phpMyAdmin in your new hosting account and select the database which you have just created in the left-hand sidebar. Hit the Import button in the top menu and choose the saved database.
At the end of the transfer process you need to connect your website to the database to update the configuration file. For these purposes open the wp-config.php file on your new hosting.
Find the following lines and replace them with the ones you have saved previously.
Next, you need to change the database name. username and password. Your localhost may remain as it is: database host stays the same since the majority of hosting providers use localhost. As soon as this is done, your files will be connected to the database.
To avoid possible downtime when transferring your website to another hosting, make sure you change your server DNS only after the whole process is finished. Having transferred databases and files, you need to change your server DNS.