Has anyone in this community been through this book in its entirety? I started it about 18 years ago when I was just beginning undergraduate mathematics study and couldn't make any headway past the first three chapters.
Now before you all start asserting that this is a much more advanced text than the undergraduate level, let me just say that even now, with the benefit and maturity of graduate studies I still have trouble getting past chapter 5 in this text. I realize that this is a concise, condensed presentation of results (hence the scarcity of examples) but my problem with this text is the complete lack of motivation for its results. Take for instance the Consistency Theorem and Herbrand's Theorem in chapter 4. I've tried hunting down the original works where these results first appeared, for more background and examples, but these works either not available or, when they are, they're too obscure to read.
Reverting to other, more elementary texts, is of no use either. They're either too elementary and deal almost exclusively with the basic predicate calculus (as if everyone needs a new text daily for THAT), or are equally inaccessible and by the time you master the author's favorite notation you're already lost in the abstraction.
Is there any hope for material that introduces the advanced results more gradually, through background and examples, and more importantly through motivating questions? Motivation would be especially helpful with the advanced results of model theory presented in Chapter 5.
Shoenfield's book is rather notoriously tough going.
Over fifty years(!) after publication there are quite a few nicer alternatives. Hodel, as recommended by @Nagase is respectable but patchy: it would not be my a first choice -- see http://www.logicmatters.net/tyl/booknotes/hodel/
On the whole I'd recommend looking for accounts in different books of (i) FOL and elementary model theory, (ii) computability and formal arithmetic, and (iii) set theory. [Merely notational differences between texts shouldn't really give you pause: a quick skim is usually enough to pick up local idioms.]
You'll find a detailed 2020 guide to books suitable for self-study at various levels in those different areas linked here: https://www.logicmatters.net/tyl/ (last updated, as it happens, a few days ago). This Guide is long, but you should find (I hope!) enough signposts to the parts that are relevant to your interests/your mathematical level.