I think that a big part of spiritual awakening (and my definition of spiritual awakening is when we begin to realize that universal truth is inside each of us, not outside) is connecting with the Higher Self on a regular basis. It's basically having the habit of carrying on an internal dialogue with the part of you, the eternal part of you, that doesn't reside in your body. It's the part of you that existed before you were born. It's the part of you that will exist after your body dies - the soul, the Holy Spirit, the True Self, the Higher Self - whatever you want to call it.
And I call this internal dialogue prayer. I don't think that prayer is about getting on your knees and asking some sort of "Santa Claus-God" for things or experiences. "God, please bring me a new car." "God, please let Aunt Mary be okay." Nope. Not prayer in my book. What prayer is is quieting the human mind and listening to that higher part of you. Prayer is connecting to and having a relationship with your soul. And it isn't about things or experiences. It is about a state of being. It's about communion and connection with spirit.
And I've found that the most important kind of prayer is of gratitude. So, this doesn't mean making statements about gratitude. "Thank you for my new car." "Thank you for Aunt Mary's health." Although you can say those things. A powerful prayer is one that is felt, not stated. Feeling grateful for your things. Feeling grateful for the health of your family. That's an important kind of prayer. Being in a state of gratitude, living every moment of every date fully grateful for everything - that's the most important kind of prayer.