I like that model and use it often. What I'd like to comment on today is the difference between Praise and Thanksgiving, because often I've noticed that when we use this prayer model in united prayer, these two categories often run together. We tend to praise God for healing our sister from illness, or praise Him for the rain or sunshine we got, or praise Him for our homes or food or whatever. There is nothing wrong with this. But if you want to take it to a deeper level, you can differentiate between Praise and Thanksgiving.
We give thanks for things we've received from someone else--gifts, blessings from God, etc. It's for things that relate to Me. Praise, however, is showing an expression of adoration to the other person, or God, for what they are, with no relation to what that person (or God) has done for or given Me. For example, if my husband does the dishes or runs an errand for me or gives me a gift, that's Thanksgiving. But if I tell him that he has beautiful eyes, or a lovely smile, or I admire his strength in a certain situation, or just simply look at him and smile, that's Praise. It's all about him, and is completely independent from anything he's done for me or given me.
I've found that it's harder to praise God than to thank Him, which is probably why Thanksgiving and Praise tend to run together in prayers. We mostly know about our own human experience, and who God is in Himself is much harder to comprehend, so we thank and "praise" Him a lot for what He has given us and done for us. We should do that! But if we take the mental effort to try to praise God for something completely independent from what He has done for us (even our salvation!) we find that we have to dig a little deeper.
How can we praise God? The answer is that we have to know as much about His character as possible. We can also take clues from Scripture such as the book of Psalms. We should spend much, much more time than we do in thanksgiving for what He has given us and done for us, but it is also an excellent mental exercise to work on praising Him for who He just is, apart from what we get from Him.