Transfering websites from one webhost to other

This will help-

I presume you have cpanel shared account

1) Log into cpanel and select "Backup Wizzard"
2) Select Backup option then "Full Backup"
3) Then you have a few options but select "Remote FTP Server"
4) Enter a email that will let you know if the backup was done successful
5) Enter the ip address in the "Remote Server" block
6) Enter the user name in the "Remote Use" block
7) Enter the password in the"Remote Password" block

5,6,7 You can get from your new hosting company or it should be in your welcome email.

Then generate you backup.

8) Contact you new host and tell them the full backup is on the new account and ask them to restore it. (you cant do this)
9) Change you DNS to the new host
10)Wait a minimum of 24 hours and ping your domain on the new account. If the results returned is the new IP of your new host you OK and the DNS is changed.
11) Test your website on the new server to insure it is working.
12) Only then cancel your hosting with old host or delete the content of the old host

I take it you on a shared account as if you were on a dedicated server with full WHM access or a reseller account you wont be asking this. Never take for granted when you do a backup that all will be well on the new host. First test all on the new host before you delete your old data as once deleted it is gone. There is no recycle bin on a server.

If you trust your new host give them your cpanel login codes and they will do it for you. If they want to charge you go somewhere else.

If all fail I would be glad to assist you at no cost to you