Q1 this happens a lot by accident Q2 this happens a lot in older game in games that you can emulate (like mario party) you can check sometimes if something is rng by savestating(ex. Mario party 1 if you savestate before rolling the dice) there are also a lot of programmers who look in to the code to understand what manipulates what

I am unqualified to answer Q2. Regarding Q1, just wanted to add that a lot of times games from the same genre share common trends, even if they run different engines. Take tile-based 2D platformers - wall ejections are a fertile ground, so any time you have a tile that is not a four-sided wall, it's worth exploring whether you can get "stuck" in walls. Clipping in 3D platformers is similar - corners and texture borders are often gateways to new possibilities. Trial-and-error, exploring obscure nooks that the developers might not put time into, and lots of repetitions will eventually yield an aberration that you can reproduce!

Q2:

Allot of people use emulators to check what the RAM looks like since allot of emulators have that feature. When something is changing inside the game, it's always stored in the RAM, so you gotta take a look there. Of course, there's allot of stuff in there, such as all information about your character (health, speed, states, etc.), your enemies (position, health, etc.) and in sometimes games sprites (graphics) as well.

By observing the RAM on ever change (For example getting hit by an enemy 300 times on purpose), you can check which position your needed information is stored. Good example for that would be PKMN-Inventories. When you mess around with it enough, you notice that the values in there are way off from what they should be and may result in Integer-Overflows. When that happens, usually all the magic starts to begin ;)

Now, for newer games that's quite hard. Since new games are running on current tech platforms, you can't look at the RAM that easily anymore. Consoles don't allow you to run custom code that easily (So you can take a look at the RAM) and on the PC it's hard/nearly impossible to ONLY show the RAM-Section the game is using. Everything is mixed and way more complex now, so there's no practical way (at least on my stand of information) to get the data from the RAM. So the once thing you can do is mostly trial and error. Allot.

Q1: Literally just mess around as much as possible. Try anything and everything and if something seems suspicious investigate it. Sometimes, it just happens randomly, and if you notice one occurrence, investigate in-depthly. I found a helpful glitch in Antichamber by just testing a possible strategy for someone when I noticed an outcome I wasn't expecting and everything progressed from there.

I would try to explain Q2, but I don't think I'm qualified enough :P @PreFiXAUT 's explanation is well written, though I should add that modern games tend to have pointers to values in memory, so finding pointers can help.

GDK

To find glitches you must think like a programmer. You must know about common bugs that programmers can overlook. You can mess around mindlessly, but that doesn't always yield the best results. Having understanding of computer logic can be a great asset to glitch hunting.