In order to be happy, we need to be ourselves. It may seem paradoxical, but to be able to be happy, we do need to allow also our unpleasant feelings. How can you be genuinely happy when you're not completely yourself, dissatisfied with the feelings that are actually there deep inside? If we don't allow all of our feelings, we can only have a superficial sense of happiness, with suffering going on under the surface, leaking out into our awareness every so often.
Feelings only stay forever if we suppress them. They will then stay in our unconscious. If we do allow ourselves feeling them as they come up in the moment, they'll run their natural cause, which means that they'll eventually dissolve. This doesn't mean acting them out, though that can in certain instances help becoming aware.
Being in touch with your feelings
Being in touch with yourself means that you face inconvenient truths and unpleasant feelings, when that is what reality is. This is the hardest thing to do. The information in the other sections of this site can help you with that.
Spirituality is ultimately about being real, and thereby being yourself. Enlightenment is the most radical way of being yourself. There usually is a place for meditation in spirituality, to help you become more aware of yourself.
In meditation, you concentrate on a particular point in your body. When you notice that your have drifted away from this point of concentration, usually by thinking about something, you gently return to it. See for more details on how to meditate, the page about meditation.
By meditating, you learn to become more aware of what's happening in you, and to stay present with that. You learn to be more in the moment, and just be with what is there. Over time, this makes you calmer and more relaxed, and more yourself.
A.H. Almaas's Diamond Approach
The books written by A.H. Almaas, that describe his Diamond Approach, can be particularly helpful with becoming more self-aware. Central to the Diamond Approach is the Inquiry practice, where you investigate what goes on inside of you, and thereby make the unconscious conscious.