There are 4 ways to increase strength according to the science and principles of strength training by zatsiorsky. That book might be a meme but I read it eight years ago and this always stuck with me.
Max effort - low reps, pretty obvious. Lot of different ways to do this and they all involve some flavor of 10 to 30 reps for singles, doubles, or triples. Powerlifters are 100% the best people to ask about this, as they have gotten the fatigue and nervous system management down to a science. You can't peak your strength forever, of course.
Lifting to failure - classic, also obvious. Bodybuilders do this more or less all the time. My general favorite method of training because I just go til I cant, don't even have to count reps. Anywhere from sets of 6 to as high as 30. Probably the most brainless approach and lends itself well to what I call "lifting for fun".
Lifting a weight with maximum speed - a lot harder to effectively program or do safely so this is out for most people. I suppose hill sprints for the legs might do this. Picking up a moderately heavy sandbag and slinging it over the shoulder as hard as you can also does this. Squat jumps with a barbell, push presses with the barbell, cleans I suppose. Oly lifts aren't recommended without proper coaching, but oly lifts with dumbbells are a lot less technical because you dont have to shimmy your body around a bar at speed. The focus is on maximum speed so when your reps slow down, you stop. Do not grind these.
Submaximal lifting for submaximal amount of reps - so for example 5 sets of 8 reps of a weight that you can comfortably do. Tends toward larger volume, I'd recommend no less than 30 total reps per mpvement if not more. Do that for 6 to 8 weeks then bump the weight up a bit. It is very easy to phone it in with this approach which is probably why I never grew a cape and flew with this method. Gymnasts apparently favor this and they call it "steady state" training.
Pick one method and grind it out til it stops working, then pick a different one.
As far as methods.
The strength training modality with the most carryover to everything else is probably sandbag lifting, since they are so wiley to pick up with the hands. The center of gravity is far away from yours as well. You need strong arms and a strong grip to lift them. As Brian Alsruhe says, if you can lift a 300 lb sandbag, you can lift a 300 lb anything.
So for all the "functional training" guys out there and for whatever reason, that number seems to get larger by the day, if you don't want to pick up heavy iron but still want very useable strength, pick up somewhat less heavy but no less challenging sand.
A good sandbag can be bought or built and the cost of sand is pennies on the dollar compared to iron.
Or you can be terrible like me and buy them off ali express about 80% cheaper than you can buy them from american companies that just stitch their name on the chinese made sandbags.