Select the xdelta file you downloaded when prompted for a "Patch". Select your Nayuta no Kiseki ISO when asked for a "Source" or "ROM".
Be sure to supply a name for the output file that ends in ".iso" or ".ISO" so that the patched file is recognized by PSP CFWs and emulators.
If xdelta3 is already installed on your system elsewhere, you should also be able to run something similar to this:
xdelta3 -ds original.iso patch.xdelta patched.iso
These are all issues that exist in the original fan translations:
Boss and new area intro graphics still untranslated (example).
Erasing save data from in-game menu doesn't work.
Strange text spacing in some longer spell and item descriptions (example).
Long achievement names are cut off in the notification box when unlocking them, e.g. "armor of anhillat".
The above two could be solved by shortening them, but I'm not willing to butcher them further.
Characters that use idiosyncratic manners of speaking in Japanese probably still don't here.
E.g. Geo is supposed to sound like an old man (characters even comment on it several times in-game), Eris is supposed to sound domineering or something. Algol and Nemeas are definitely supposed to sound unique too.
Noi has her own verbal tic that is lost.
Things like slang or shifts in politeness or tone are probably still not accurately conveyed.
Text speed isn't as synced to voices as it is in Japanese (text speed should still be modified to be faster than the voices, if anything).
Edit 2: Disabled xdelta secondary compression. Web and Android patchers that do not support this should now work. *Also includes everything up to here.
v1.06 2021/03/11
Fix erroneous 'Obtained mirareceived..' message introduced in 1.05 (a106020).
Redo some museum descriptions, focusing on better scientific accuracy (826f513).
Dinosaurs aren't usually described as having fangs, cobras don't have a special noise-making organ like a rattlesnake, etc.
Sneak in some consistency fixes and two single-letter name changes (03649eb).
Fixed extraneous Japanese text at the end of Volans' sidequest.
Fixed bug that prevented talking to Mishy at some points.
San Ceriz -> Saint Cerise.
Major locations whose names start with "San" AND "Sento" in Japanese are both rendered as "Saint" in official localizations.
Dr. Volans -> Professor Volans.
fixed typos, such as those in #4, and other relatively small text changes.
v0.9.2 2020/11/15
Translate Japanese text in graphic that appears during final boss fight (fix #1).
Fix some inconsistencies and errors in food and achievement names and descriptions (fix #2).
Fix some graphical inconsistencies in the manual and chapter 5 titles (fix #3).
Redo names and descriptions of nearly every piece of equipment, spell, and monster.
Fix ingredient locations using the partial English text from old fantranslation, they should now entirely in English and relatively (there's not as much screen space) consistent with current dungeon names.
Numerous other minor text changes.
Big thanks to @Wandering-Heiho for help with locating or editing some of the graphics.
v0.9.1 2020/11/01
Confusion status effect is renamed to Panic so it is consistent with the animation. The manual graphic is also changed to reflect this, increasing the size of the patch.
There's also some minor text edits, mostly to fix typos, missing words, or repeated words. That's what I get for doing a spelling and grammar check after after my first pass, making a bunch of changes, and then not doing a check afterwards.
v0.9 2020/10/28
v0.9 because there are still outstanding issues that don't exist in the original translation.
Use 4.15.xdelta to patch the ISO with 4.15 release of the original translation, or use clean.xdelta to patch a clean Japanese ISO.
Credits
Based on the work of a previous fan translation project:
Flame - Project leader, main programmer, translator.
SkyeWelse - images.
naachan - translation assistance - helped with boss, character and location names.
Kelebek - programming assistance.
CUE - programming assistance.
zero_g_monkey - programming assistance (images).
M_bot - image programming.
This project:
Wandering-Heiho - video editing, image editing assistance.
Also thanks to anyone who reported any specific issues.