I'm going to talk about using a manual brush today it is much harder to do a good job with a manual brush than when using an electric one.
With an electric brush - either sonic or oscillatory - you just have to put the bristles next to each tooth surface in turn and let the machine do the work.
With a manual, it takes a bit more effort.
There is no single brushing technique that is universally agreed to be the best (If it removes all the plaque and debris without doing any harm, it's good.
If it doesn't, it's not) Here's one method that's proven to work:

• Use a medium toothbrush - a hard one will cause damage and a soft one may not shift everything you need to get rid of.
  There are cases where a soft brush is advisable and, if that applies to you, the hygienist will advise you accordingly.
  The brush should have a small head so you can get it into all the nooks and crannies and into the tight areas at the back.
  
• Hold the brush so the bristles point towards the gum at 45 degrees (by the way, modern brushes don't have actual animal hair 'bristles'; they have synthetic filaments, which are much more hygienic.
  But 'bristles' is a convenient term so I'm going to keep using it)
• Use small circular or vibratory movements, gently pressing the bristles into the spaces between the teeth.
  
• Clean every surface of every tooth - cheek side, tongue side and biting/chewing surfaces.
  To do this properly, you need to address each tooth - or at the most, every 2 teeth - separately.
  If you try to brush a whole area of your mouth in one go, you will not get all the teeth clean.
  Take particular care to brush the tooth where it contacts the gum.
  To do this, you will need to brush the gum as well as the tooth.
  This may cause bleeding - but don't stop brushing.
  The gums are bleeding because of irritation from plaque and the only way to settle them down is to remove the plaque.
  Remember: healthy gums will not bleed when you brush them.
  
• If the bleeding continues after a week or more of thorough brushing, see your dentist.
  
• Don't forget to change your toothbrush regularly.
  The general recommendation is that brushes should be replaced every 3 months but if the bristles start to splay or bend outwards before then, you need a new one.
  

Follow this simple plan and it will make a big difference to your oral health.
It isn't rocket science but, in my experience, the problem isn't technical; it's to do with attitude.
Some people think: 'I've been brushing my teeth the same way since I was small child and it hasn't done me any harm, so why should I change?' Well, I see the results of that approach on a daily basis and, trust me, they're not pretty.