They're very similar in the pattern of working out proofs.
That's what I remember over 30th years ago in intro to logic (philosophy course not math or comp-sci) being similar to my 9th grade geometry class proofs.
The skill to work on in an intro class is to make sentences out of the logic propositions and then work on making ordinary sentences into the logic notation.
Additionally, as when learning anything mathematical, don't expect too much help from Wikipedia. Pedagogy often involves telling small lies to students at first, then clearing them up later. Wikipedia has a bias towards being correct, which means that the articles can't tell those small lies and the explanations are difficult for non-experts to understand.
The about page states that the book is for "an intermediate level (i.e., after an introductory formal logic course)." It'd be advisable to look elsewhere first if you don't have any exposure to propositional logic. For example, the first eight chapters of MIT's Mathematics for Computer Science textbook should be sufficient: https://courses.csail.mit.edu/6.042/spring17/mcs.pdf
The standard tip for reading mathematical texts is twofold: always try to come up with a proof before reading the one supplied in the text, and never ignore the problem sets. As Pólya famously put it, mathematics is not a spectator sport.
EDIT: s/"How to Solve It"/"How to Prove It".
Velleman wrote "How to Prove It": https://www.amazon.com/How-Prove-Structured-Approach-2nd/dp/...
Polya wrote "How to Solve It": https://www.amazon.com/How-Solve-Mathematical-Princeton-Scie...