1> First of all, we will suggest you to contact your new hosting provider and ask them about this procedure. There may be some other steps involved than our provided.
2> Now, sign up with your new hosting provider.
3> Get the name server details from your new provider.
4> Then provide those details to your domain registrar and ask them to point the domain to these name servers.
5> It will take maximum 24 to 48 hours to propagate the name servers over the Internet.
6> Meanwhile, you can take the back up of your hosting account from your current provider to your local computer.
7> And then you can upload the backup to your new hosting provider.
8> After propagation, you will be able to access your web site from your new provider.