Using texture replacement packs
If you're looking for information on how to create texture replacement packs, see here.
Finding texture replacement packs for your game
The best place to find packs is currently Texture Replacement Packs forum in the PPSSPP forums.
Installing
To install a texture replacement pack, just open the zip file directly in PPSSPP, as if it was a game. Use the games tab or the Load... button.
PPSSPP will take care of installing it in the correct location, and unpacking it if necessary (PPSSPP now supports reading from zip files directly, if textures.ini is in the root directory of the zip).
If you want to install a zipped texture pack manually, create a folder with the game ID in TEXTURES (such as NPJH50505), rename your zip to textures.zip, and put it in the folder.
You can also install manually. The place for textures are in PSP/TEXTURES, in subdirectories by game ID (without hyphen).
Using
Make sure this setting is enabled: Settings > Tools > Development Tools > Replace textures
Then just start your game.