Michael Horton’s God of Promise, chps. 3-4, puts the big blocks of his thesis in place, and the big blocks are not hard to understand, and they go a long way to explain how his understanding of covenant theology works.
First, there are two kinds of covenant in the OT:
Promissory Covenant with Abraham: also Adam (after the Fall), Noah, and David. So, each of these covenants is a promissory covenant in which God makes an unconditional promise apart from any stipulations and conditions on the part of God’s people. The emphasis is on God’s promise, God’s oath to do what he says.

Genesis 15 is not simply a suzerainty treaty but a royal grant from the human side but a suzerainty treaty from the divine side.
The New Covenant, with Jesus, is a promissory covenant.
Law/Works Covenant with Moses at Sinai: God forms a suzerainty treaty with Israel at Sinai that stipulates the conditions (the Law) under which Israel must live if it wants to live in God’s blessing in the Land. This covenant had a limited time (Moses to Christ) and a limited purpose (typological manifestation to lead to Christ). This covenant is conditional. The emphasis here is on the oath the humans make to do what God has commanded.
Covenant theology provides for a reader of the Bible a comprehensive grasp of the big picture (if it is accurate). To read the Bible we need, so they suggest, to distinguish between the conditional covenant and the unconditional covenant.
A significant text here is Galatians 4:21-31 where Paul speaks of the covenants with Hagar and Sarah, and then of law and promise, and so on. Here is a clear indicator for Horton that this hermeneutic of covenant was at work all along: from beginning to end there are two covenants at work.
For readers of the book: Horton’s book is an intramural dialogue between covenant theologians; there are not other serious discussion partners for Horton’s book. It is largely the dialogue that goes on within the walls of a place like Westiminster between folks like Geerhardus Vos, O. Palmer Robertson, and the like. He relies often on Delbert Hillers and Meredith Kline.
Also for the same readers: if you do not know the discussions between these folks, this book will have sections that will be meaningless or quite difficult to comprehend. I recommend that readers first read, say, the article on “Covenant Theology” in Baker’s Evangelical Dictionary of Theology.