CD-ROM, Flash-ROM, DVD-ROM... the Read Only Memory part of it kind of says it all there. Which is to say you don't.
Some devices have an optical drive emulator that you can load games on, and some devices might have a cheat device you can patch some things on the fly with (think cheats rather than full translations) but most people, assuming they are not using an emulator, will mod their device to accept burned games and burn a modded version of the ISO (which you may or may not want to rip yourself). I don't know what we are currently suggesting for PS1 mod chips, cheat cart methods, or if there are any optical drive emulators worth paying attention to. If doing anything with the laser I hope it still works -- the PS1 lasers were not known for durability even when they were current and burned discs are harder to read.
The PS1 is additionally a nightmare for some things here. Back when the PS1 was current we did not have any particularly well followed Scene rules like we have for later systems, and additionally every other tech company was seemingly trying to muscle in on the CD writer boom and one of the ways to do that was to support PS1 games (usually heavily unofficially, or with "we support game consoles" in the features list).
In addition to plain iso and bin+cue you got half a dozen other formats like Nero's NRG format, Clonecd's CCD, cdrwin, cd juggler and all the other formats the likes of ultraiso will claim support for. Any given game seemed to be ripped in any number of formats, and they persist to this day. That or people get bored of that and rip it again in plain ISO.
You will also encounter a bunch of different patch formats (PPF, bsdiff, xdelta and a few others) or be told to grab individual files from the game and patch those (this is rarer but far from unheard of). Usually that is a matter of getting the right iso, the right patch, the right patching program and pressing patch.