"[Pray] at all times and on every occasion"
How do you talk to your best friend? Do you only call on her or him when you need something? Do you begin every conversation with formal dialogue God doesn't need the formalities all He needs is you to reach out and communicate with Him.
God wants to be your best friend -- the person you can't wait to talk to, the one you look for advice, the one you can't spend a day without thinking about in some way. Don't let the formalities and the way you "should" speak to Him get in the way of actually speaking with Him. He wants to know you and hear from you all the time about everything.
Prayer to me isn't a formula to memorize and rejuvenate Prayer is just like breathing. It's something you don't really think about, but you simply constantly do.
One of the best examples of this is when I see a wreck on the highway, my automatic response is to lift that person (or people) up to God in a breath of prayer -- "Dear Lord please be with them now as they face this trial before them. Give them strength and peace."
That's it. God knows that I'm genuinely concerned because He knows my heart. I don't have to dwell on the formalities. I am in constant communication at all times with God and I pray during all occasions.
You don't have to put things on a list until you have time to make a formal request. I used to do this and the result was that I would never pray at all. All the parts of prayer -- the adoration, supplication, thanksgiving, intercession and confession -- are all important, but they are all there at all times. You don't have to go through them all every time you talk to God -- when you pray at all times in every occasion all of the parts are covered as they come up.
The point is this -- prayer is simply communicating with God, just like talking to a friend.