It is very easy to swtich, all you need to do is to sign up. You would need to make an arrangement with MWEB about keeping your email accounts with them. We will also give an email address which you can use to forward all your MWEB emails to. You can also create an auto responder. This will help you tell everyone that you are now changing your email address to ***@afrihost.co.za. The auto responder that you create will be sent to everyone sending you an email to notify them of your new email address.
Alternatively you can sign up a domain and use it for your emails and probably create a website at a later stage. This will help to never change your email address ever again. This is the best way of controlling your email accounts. If you have a domain and you want to transfer all the email accounts with, you would need to sign up the domains as a transfer and restore all all your emails again.
I hope this answers your questions.