Please advise what is a good teeth cleaning method?

Good oral hygiene. To achieve that you need to have a checkup and a cleaning at your dentist twice a year, with following proper oral hygiene by properly flossing then brushing your teeth and gums and tongue, proper diet also help..
See Dentist. First see dentist for evaluation of teeth and supporting issues. Then have teeth professionally cleaned. Then dentist/hygienist can advise you of the best way to keep your mouth clean. Everyone, s different, and require different techniques, so ask your dentist.
Brush and floss. Brush those suckers until all the plaque is off. This is nor rocket science.