The opposite of happy is not sad. The opposite of happy is negative.
You can be sad and happy at the same time. You can even be depressed and happy at the same time. But you can't be negative and happy. Happiness, however you define it is positive. It requires upbeat thinking and feeling.
Although you need negativity as a survival mechanism, it is primarily defensive. It causes us to withdraw. Take shelter. Hide. It was very good at helping us avoid being eaten by saber tooth tigers in prehistoric times. It's still good at preventing us from taking action too soon or fighting when we should flee.
But because you perceive so many risks in your everyday life, you may end up with a lot of worry and anxiety. You may anticipate so many problems with your possible choices that your fear of risks keeps you from achieving a positive outlook in anything.
You get caught in a self-defeating loop of "I can't do this, because..."
This is why positive thinking works.
Not positive thinking as in platitudes and pep talks. But rather replacing negative thoughts with positive reasoning. Negative thinking blocks action. Blocks problem-solving. Paralyzes.
Positive thinking, as psychologists currently define it, is looking for your own strengths and virtues and finding the ones that help you succeed. Not just in general. You also specifically look at whatever your circumstance or problem is and find the skills and strengths that help you resolve it. You get help from others that have the strengths that help you resolve issues and build successes.
You stop thinking "Oh my gosh, this is so hard!" You start thinking about what would make it possible, probable or even easy. You start looking into yourself as the source of what makes things possible, probable or even easy.
You can't keep an optimist down.
Why? Because an optimist finds reasons for a positive outlook and sets out immediately to succeed and prove he's right. He focuses on his strengths and uses and builds them. He works to correct his weaknesses. He looks for and accepts help from others who have strengths in areas where he may not perform as well.
If he's trained in realistic positive thinking, he fully examines risks and plans for handling all probable outcomes -- positive and negative.
No matter what happens, an optimist is still happy. Because he constantly seeks the positive outlook and takes action. He is always working to perform better. He is always able to produce some positive outcome. He has power in his own life.
The current field of Positive Psychology, organized by Dr. Martin Seligman, teaches you to find and examine your strengths and virtues and build upon them. To achieve a positive outlook and be as happy as you can be. There is a great deal of literature available.
Dr. Seligman's books Learned Optimism: How to Change Your Mind and Your Life and Authentic Happiness: Using the New Positive Psychology to Realize Your Potential for Lasting Fulfillment are foundations for studying positive psychology. They are meant to be read by a general audience interested in self-improvement. I recommend them.
But if you'd like to know more about how happiness affects your life, work, performance and productivity, and you'd like something that summarizes the field to date and is an easy, fast read, you might also try Lynn Johnson's ENJOY LIFE! Healing with Happiness.