Higher metabolism rate helps lose weight
and burn fat at rest

The main way to speed metabolism rate is by building muscles.

By doing regular power work out like weight lifting ,you will gradually increase your muscle mass .Muscle tissues need more energy than fat tissues. Therefore if you increase your FFM=Fat Free Mass ,or in other words you build muscles ,then your body energy needs will rise. Building muscles is not a short term process it's gradual and need to be monitored.If you exercise and don't change your calorie intake than in the long run you will lose weight.
The body main energy source at rest is fat. Therefore a more muscular person will burn more fat at rest then another person in the same weight but with less muscles (with more fat ratio).
To make sure the body burns fat and not muscles keep these in mind:

Eat every 3-4 hours, small to moderate meals.

Do not skip meals.

Power workout does not necessarily mean weight lifting .It can also be done with the body weight ,especially for children. .In water old people, people with back problems and others who can not lift weights ,from any other reasons. In any case consult your physician and a certified trainer.

Watch your calorie intake carefully. It's well known that when people start training they feel like they have worked hard and deserve a big good meal right after. Good and healthy meal is fine but a big meal might result in not being able to lose or even gain weight. One big meal once in a blue moon is not a problem since gaining weight is a gradual process . Our body is very smart but can not be cheated .Every day ,24 hours a day the body checks out its balance .
Energy intake (food and drink) minus energy expenditure (for body maintenance and activities).If the balance is positive we gain weight ,if negative we lose weight. Losing and gaining weight is done all the time 24/7 .Only scales sensitivity determine if we see it on the scale or not.