Cowen's History of Life
Your best bet is Cowen's History of Life, it is an excellent introductory textbooks for paleontology well laid out and clearly written with introductory students in mind so a laymen will be fine. It covers the entire breadth of the life. Check the edition though there are six of them now and the older ones are pretty outdated and not laid out as well. if it wasn't so expensive I would buy it to give to people.
I can recommend a few more specialized texts, to dig deeper [pun intended]
Terrestrial Ecosystems Through Time: Evolutionary Paleoecology of Terrestrial Plants and Animals which is an excellent review of terrestiral life.
Invertebrate Palaeontology & Evolution
by Clarkson which is a beautiful textbook yet still accessible to the laymen since it is written for undergraduates.
Introduction to Paleobiology and the Fossil Record by Benton and Harper is the best introduction to paleontology in general you can get, and may be worth a look if you are having trouble with the other books make.
A lot of searches will point you to Life: A Natural History of the First Four Billion Years of Life on Earth It is OK but the author very much has their storytelling hat on. Great for making it a more enjoyable read, bad if you want information. It reads more like a biography.