To move your website you need to download all your website files, and databases if you have them.
Then upload the new files to the new web host and then import the database into the new hosts server.
To make it easier a lot of web host companies will move your websites over to the new web host for free.
Look on their website or even just ask their tech support if they'll move your website to the new web server.
They'll do all the heavy lifting and you won't have to do anything except changing your dns servers name at your domain provider.