I've tried to write a definitive guide to traps for players in OSR-style games a couple of times, but struggled to compose something complete and engaging. Therefore, what follows will be unstructured and incomplete.
Proviso: there are many ways to play tabletop dungeon games. The way your DM runs things is not the way I run things or the way you run things or the way anyone else runs things. Accept their unique style with grace and adapt to it.
In general, we can say that every trap has a trigger, the cause or catalyst of the action; a mechanism, the means of the action; and the trap itself, the negative consequence of the action.
Triggers are almost always the result of a character's behavior when they interact with something. You can keep this in mind. The trigger of a trap is almost always something that a DM (or the NPC who set the trap) thinks the PC might do. A trapped chest is more likely to have a trigger designed to go off when you open the lid, pick the lock, or remove the entire object than one designed to go off when you get it wet, sit on it, or rotate it. Think about the environment's affordances.
Often, the triggering behavior is a surprise but the triggering object is apparent. Consider what the DM describes about an area. Is the floor mentioned, even just to say it is composed of tiles? Is there any sort of artificial mechanism, even one as simple as a hinge? What would I guess you might do?
You will sometimes have to trigger traps intentionally. They might guard treasure, block access to other sections of the dungeon, or have potential use against enemies. The best way to trigger a trap safely is to be as far away as possible. Maybe you can pull a level with a loop of rope, standing 100 feet back. The second-best way to trigger a trap is to be standing in an unintuitive spot. When you stand behind a treasure chest and open it that way, any spring-firing darts loaded within will totally miss you because you opened it in a way the designer did not intend and stood in an area they did not target.
There is a corollary to this: beware of gas weapons. Gasses fill the volume of their container, which is to say the dungeon chamber and your lungs. If you expect to deal with poisonous gas, you might be able to hold your breath or inflate a pig bladder for air or something. But even this is not a sure thing! Some gasses are corrosive or acidic, and damage on contact with the skin or eyes.
Mechanisms are tricky to deal with because they are usually the part of the trap that is least-described. DMs don't usually have a diagram showing exactly how applying pressure to a tripwire causes spears to shoot out of the wall. But if you can interrupt the working of a mechanism, you will usually have neutralized the trap.
If you have a good guess of how the trigger works, you can try to render it inoperable or disconnect it from the rest of the mechanism. Some tripwires, when snipped, are ruined. Some trapped locks can be sawed out of their housing.
You don't need to disable the trigger to disable the mechanism. Every component of the trap has the potential to be disabled. If there are suspicious holes in the wall, you can plug them up even without knowing what causes bolts to shoot out of them. If you have the time, disable as many stages of a trap's mechanism as you can.
Unfortunately, many of a trap's inner workings will be hidden behind walls and under the floor. Be more suspicious of rigid , flat surfaces like cabinet sides, sarcophagi, and trapdoors, than you would be of soft and flexible material like sackcloth and flesh.
Worse yet, magical traps typically have no mundane means of being mangled. Magic traps can summon objects from thin air or detect actions far more subtle than mechanical means normally allow. If you have the means to dispel magic, great. Otherwise, be aware that some traps have otherworldly mechanisms that you cannot interact with, and will require other approaches to deal with safely.
Traps proper are the payoff of the whole production. Until you have seen a trap go off, never assume that you know exactly what the trap will do. If you get out of the trajectory of a series of holes expecting bolts to fire out of them, only to be met with corrosive gas, you'll feel like a fool.
The easiest traps to deal with are projectiles and blades, because you can try to disable the trap with danger zones in mind. Other traps, like fire traps, acid, gas, spell blasts, are tricker to deal with because they can affect a general area, and you may need to be within that area in order to manipulate the trap mechanism.
Still other traps don't attack their target at all. They might activate a falling gate that blocks the way out of a dungeon or do other disadvantageous things that bring on incidental danger. You're usually safe from this kind of trick if the mechanism can be picked up and moved somewhere else, but if it is built into the architecture you must assume it can affect that architecture until you understand how it works.
Smashing up a potentially-trapped container to bypass the mechanism is often possible, but often undesirable. Unless you can take it out of the dungeon before attempting the maneuver, you risk spending time and making noise which can attract dungeon monsters. The contents can be damaged if you breach a chest with an axe or a sledgehammer, shredding scrolls and shattering potions. If you can take your time, you might be more likely to succeed with an awl, a saw, or other means of breaching the container without smashing it apart. This is where those rigid, flat surfaces can work for you.
Over the course of a campaign, try to keep in mind the sorts of triggers, mechanisms, and traps you encounter. There will always be novel problems, but the same DM in the same milieu will usually repeat certain common elements. When you learn how to spot potential triggers, mangle mechanisms, and avoid dangerous trap effects, you'll impress your fellows and enrich your coffers. Best of luck.
You are ready for A D V E N T U R E !