Moving from one hosting provider can be a headache for novice users, who are not aware of how to update name servers.
Follow these steps and you will save yourself some frustration:
1) Find a hosting provider after doing some good research, don't jump on the cheap bandwagon. Do some research, view feedbacks from other users. The most important thing for any hosting provider is their customer service, so make sure your hosting provider has a online chat, phone number to get in touch during emergency.
2) Once zeroed down on your new hosting provider, sign up for an account.
3) You will receive the new name servers such as ns1.yourhostingcompany.com and ns2.yourhostingcompany.com along with the IP's.
4) Before you update the name servers with your domain registrar, make sure you download your emails and webfiles from your current hosting account.
5) Login to the control panel of your domain registrar, this is where you have registered your domain name. Don't confuse this with your hosting account.
6) Go to the namserver section in your control panel and replace the old entries with the new name servers.
7) Save the settings, usually it takes few hours to update the DNS servers around the world, but max can be12 -48 hours for the DNS around the world to refresh.
8) Check your website every few hours, once you can see your new server, you can stop your account with your old hosting provider.
Any questions just post it!