First off, download (or create) the map you want to install. Kurok should be compatible with most Quake 1 maps, and will automatically convert things like weapons, healthpacks, and viewmodels to their Kurok equivalent.

Plug the PSP or MicroSD into your computer, and locate the "Kurok" folder. Find the other Kurok folder inside, and create a folder called "maps", and place your map inside.

Now take the PSP out of USB mode or put the MicroSD back in the device and open Kurok. Get into a singleplayer or multiplayer match (depending on the type of map you downloaded) and choose any map.
Pause the game, go into Settings > Go To Console, then press the square button and enter in the command "map *your map name here*". It should load up correctly. If you're in a multiplayer map you can even add bots!o

If you have feedback, suggestions, maps you want to host here, something else to put on this site, or a better way of explaining this whole thing then feel free to email me at customkurok@protonmail.com. Thanks.