Is it true that our metabolism begins to slow in our 30s? what are some ways to increase it again? cardio workout? strength training? diet changes?

You are spot on: Metabolism does seem to slow as we age, however, that does not mean we cannot counteract that with diet and exercise. Both aerobic/ cardio exercise and strength training play a role in boosting metabolism. A good start is 3-5 days of aerobic 45-60 minutes and 2-3 days of strength training. Add some stretching to keep it balanced. Watch fats/ sugars in diet and in all moderation. Beware alcohol.

Yes : With age metabolism does slow down due to hormonal changes and loss of muscle mass. The best way to increase metabolism is avoiding processed starch and processed sugar and eating a diet high in protein and complex carbohydrates and and fish based fat. Daily exercise, cardio 3 to 4 times a week, weights 2 to 3 times a week as well as yoga would also significantly improve one's metabolism.