The practice of meditation has been deeply misunderstood across hemispheres and longitudes. To meditate is to inquire, to investigate. To explore the mind. It is not conducted in isolation of daily activities, 15 minutes in the morning to compensate for our daily mischiefs.
Meditation is a constant mental endeavor. A meditator aims for ultimate awareness of the self, the body, and the phenomenology of the mind. Each reaction is noticed, however subtle, and it's underlying connections revealed. The meditator reaches for the divine, annihilating the ego and aiming at higher levels of consciousness and abstraction.
No one can teach you how to meditate. It is a single-player game and an art. It is practiced, not revealed. My suggestion would be to attend the longest meditation retreat you can afford (here's a list). Don't start small. Go for the shock. Be hungry and jump with your face into your the ocean of your mind. Ride through the hinterland of your brain and look around to appreciate your surroundings. Explore its most remote corners. Observe it all. Be like melting snow. Wash yourself of yourself.
A consistent meditation practice can yield mystic trances of increasing frequency (triggered during contemplative walks, listening to musical masterpieces or practicing collective mantra chanting), stronger visual depth perception and color brightness and saturation, loss of ego, enhanced physical awareness (better posture, slower breathing rate and resting heart rate), stable and hard-to-perturb feeling of harmony, the emergence of a mental space accessible through breath that boosts abstraction and perception, abundant energy levels and lower sleep needs due to the absence mental friction during the day, enhanced creativity and lateral thinking (with more frequent Eureka moments during the day), personality changes incl. increased openness, stronger emotional connections, slower speech.
A meditative mindset must be carefully maintained. Each retreat, each mystical encounter is analogous to the shaking of a snowball. Sublime, but ephimeral.
Prolonged stress-exposure can reversibly rewire the brain and tame the ability to reach higher meditative states.
If you're looking for inspiration, I would read Jiddu Krishnamurti (can start with Krishnamurti's Essential Reader [˜100 pages], and if interested, continue with Freedom from the Known, The awakening of intelligence, Think on these things et al.). He's the most "Meta" philosopher I have ever encountered. You can also read "Essential Zen Training" to learn how to sit and breath. Headspace is nice to get exercise ideas but eventually you'll need prolonged silence.
Another beautiful exercise is to sleep over a mystic poem. Read it, and ponder on it from the comfort of your pillow. See what happens when you wake up.