Also related: Obtain Sponge.
Ocean Monuments generate in Deep Oceans biomes (so Deep Ocean, Deep Frozen Ocean, Deep Cold Ocean, Deep Lukewarm Ocean) away from non water biomes. You can look for Guardian or Elder Guardian on your pie chart since these are the only places they can spawn. If it's within 5 minutes of generating, you may be able to spot one by seeing floating ink sacs since the Guardians will kill all the squids around the structure.
Elder Guardians have 80 health, meaning they take 9 charged axe hits (except wooden and netherite axes) to kill. They deal 2 thorns damage if you hit them while their spikes are up, and their 3-second laser can deal 5 damage if you don't block it in time. Bear in mind that Mining Fatigue III slows down your attack speed. Placing a block above you head means you can jump and crit on the fall down, but you need to make sure your hitbox is entirely within the air pocket. You would only need 6 axe crits if you managed to do it this way.
The Elder Guardian in the top room is best, because it is closest to the surface and is a much more confined space, meaning that you will have a quicker fight and will not have to deal with as many (if any) regular Guardians. In my testing I only ever had a regular Guardian once in the top room.
If you have 2 TNT, lighting them with a pressure plate next to the Elder Guardian is usually enough to take it down to just 3 axe hits, so you can tank the thorns damage from those and kill it all in about 20-30 seconds. You can also use TNT placed on top of a pressure plate to break into the top room if you were donged before you could break in.
Otherwise, you can kill it with just an axe and a door, which takes advantage of the fact that whenever the beam attack is interrupted, the Elder Guardian will swim to a new location before going back to idle. If you peek while it's swimming, it will turn and try to laser you again. This means that by peeking out of your door, you can get the Elder Guardian to swim somewhere you want.
Putting your door as shown in the video gives you 3 locations the Elder Guardian can get stuck trying to swim to. Often it will try to swim down the 2x2 hole in the ground, and you can axe the edge of its hitbox as it does. Getting around 6+ hits is enough, then you can tank the thorns for the rest. If you have to do it damageless, you can just get it stuck again. It can also get stuck at the edges to your left and right, but these seem to give you fewer hits on average. Also make sure you don't accidentally get within its LOS otherwise it will stop swimming to laser you.