Gary Gygax's rules-design style was situational, descriptive, and instinctive. In the traditional of "Free Kriegsspiel," when a situation would come up in the game he would apply his judgment and experience to come up with some means (most often an ad-hoc die roll, probably with some modifiers based on character abilities) to resolve it. If this ruling seemed applicable more broadly than the single situation where it first appeared then it became a precedent and was written down for future reference. The AD&D rules are, in large part, just a collection of those rulings and precedents from 5+ years of heavy playtesting.
The rules aren't systematized - different dice are used, ability scores and other modifiers are applied in different ways, sometimes a high roll is better and other times a low roll is better, etc. - and they're not necessarily consistent with each other (two similar types of effect in two different dungeons (or caused by two different spells or magic items) might require completely different rolls to resolve), and in the published rulebooks they're not really organized except in a sort of stream-of-consciousness way (for example: where is the rule for whether a character inadvertently catches the gaze of a monster located? It is, of course, in the second paragraph of the Dracolisk monster description on page 55 of the Monster Manual II!).
The ad-hoc nature of these rules, and the haphazard organization of them, has been one of the main complaints about AD&D (and D&D before it) since day one, and almost every other rpg that's ever been published (including the later iterations of D&D) has approached things more systemically, to make them more consistent and elegant. I can understand that impulse - the size and chaotic organization of the AD&D is unquestionably intimidating to new players, and if you're the kind of player (or DM) who worries about following the rules exactly as-written it could well drive you crazy, as you continue to discover new hidden rules years or even decades later. Something like RuneQuest or GURPS, where you have to keep track of 75 separate skill values but you know that every time you use one of them in the game the roll will be resolved exactly the same way (the same die roll, the same modifiers, the same consequences for success and failure), seems simpler because it's more elegant and more predictable and easier to grasp conceptually, whereas AD&D feels messier and more confusing. In other words, AD&D feels more like real life.
There are two approaches you can take to the AD&D rules. One is to try to memorize everything, or at least memorize its location within the books so you can look it up quickly. Lots of people over the decades have tried to do it (many of whom can be found still debating the minutiae of the rules at the Dragonsfoot forums), but it's really a fool's errand - because there are so many rules, and so many of them have such narrow applicability that the payoff of knowing them will never balance the investment in effort of learning them, and because something you learn pretty quickly when you get into the detailed weeds of the AD&D rules is that all of ad-hoc special case sub-systems don't really work together - there are things that flat out contradict each other, and things built on different enough assumptions that trying to meld them together produces weird or bad results in play. But mostly trying to memorize the entire AD&D ruleset is a bad idea because it misses the entire conceptual point. The rulebooks are a massive pile of precedents and examples of how Gary Gygax ruled on things, the point of which isn't for you to follow his lead exactly, but to understand the gist of what he was doing - the type of gameplay experience he was trying to achieve - and then use that understanding to make your own rulings in the same spirit.
There are some core concepts at work in AD&D: Gary wanted a game with high stakes so that both victory and defeat feel meaningful; he wanted a game where there's a tangible relation of risk to reward; he wanted a game that encourages heroic action where bold, decisive action is a better route to success than cautious timidity; he wanted a game that always moves quickly and maintains a level of tension and excitement; he wanted a game where players to have to think tactically, strategically, and creatively (and to do so quickly and under pressure) rather than just relying on math; he wanted a game where smart decisions generally trump luck but there is almost always at least a small chance of both success and failure; he wanted a game where no single player can do everything so teamwork is important; he wanted a game where the players can feel their progress over time as they improve their skills; he wanted a game with a neverending variety of fresh challenges to keep players interested even after they've mastered the basic paradigm. Once you understand all of those concepts, you can see how they informed his decisions in the rules and adventures. And once you do that then you realize that the specific rules - whether something gives a +1 or +2 bonus, whether something is resolved by rolling a 6-sided or 20-sided die - don't matter. What matters is the feel and tone and shape of the game. If you're achieving that - if the game "feels like AD&D" - then it doesn't matter whether the roll required to lasso a stalagmite while you're being carried off down a swiftly-moving subterranean stream is consistent with how a similar situation is handled in rulebook X or module Y.
The point of the AD&D rulebooks is to help the DM achieve a particular mindset and attitude by way of a lot of examples, but once that is happens the examples themselves are no longer important and can mostly be set aside. A DM who understands the concepts underlying the game will always be better off making a judgment call on the spot than pausing the game to look up in a rule book how Gary recommended handling a similar (but probably not identical) circumstance.