How do I switch from one web host to another?

If the other hosting company cannot answer your question, then you don't want to use them. We can't answer that for you.

I bought new site and I was also finding someone who change my hosting. now i do research and see that site is showing articles for hosting shifting and many other tech issues.

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The old host needs to transfer the domain to the new host. The old host will have a procedure to "send" it, and the new host will have a procedure to "receive" it. Start your inquiries with the new host.

But that's only the IP-address to which the domain is linked. It's your own responsibility to transfer the content and the data.

Purchase the new hosting.
Download your backup files.
Download your website's database.
Import the files and database to your new hosting account.
Point your domain name to the new server.
Review your site before it goes live.

Hey John!
Hope you are doing well. You have shared some steps to be followed for shifting to other hosts. Well someone in the forum already told me these and I also want to change my hosting server. These were not helping. I was changing my client's site and suffered a lot.
So, as the bibirdmanays says that hosting companies should listen to your problem. I asked them and fortunately, they migrated the site on my behalf.
So no need to panic, just select a good host and ask them to migrate the site.
Share login details of c-Panel with them, and all are done.
Ask anything you need! open to answer.

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Purchase the new hosting.
Download your backup files.
Download your website's database.
Import the files and database to your new hosting account.
Point your domain name to the new server.
Review your site before it goes live.