hi eugene,
There are several steps that you need to do to ensure a smooth transition to a new host:
1. Please ask for a temporary URL from your new host. This temo URL is truly important so that you can preview your site on their server, even before you are doing the DNS changes
2. Please upload all your files to the required folder.
3. Please restore your database on their server
4. Once everything is done, please use the temp URL given to test your site. If things work out according to your requirements, you can then initiate the DNS changes
5. Once the DNS has resolved to your new host, you can safely terminate the service and say goodbye to your old host.
If you have any problems or concerns in migrating your site, you can always seek help from ASPHostCentral. I have been using their service for a couple of months and those are the advises I got from them. Well, I managed to migrate everything smoothly and without any downtime
All the best :)