Ask your current website provider to provide the DNS records they need to be added to the domain. This is usually a combination of "A Records" and sometimes "CNAME Records".

Once you've got those, fill in this form: DNS Management Form.

You'll then need to notify your website provider to finish the configuration.

Don't worry, you don't need any technical skill for this, just ask your current provider to "Provide me with the DNS records needed to configure the GOV.UK domain to be used on our website".