The 3D programs used for making a model and texturing it are:
3D modelling:
-Maya
-3DS Max
-Blender
With them you can make models for Amnesia. (With 3Ds max animations are glitchy, with Blender you cannot make them)
Texturing:
-Gimp
-Material Editor
This is the process:
-You make the model, you set the UV coordinates to an image and then you
EXPORT it to .dae (Collada)
-In Gimp, you create the specular and normal map from the diffuse (the color photo)
-Then, in the
MATERIAL EDITOR, which already comes with the level editor and model editor and etc you create a material with the diffuse, normal and spec and you name it the same as your model.
-In model editor, Import your mesh (.dae).
The .mat file is simply a text file which specifies the textures that the game has to use for the model, and photoshop just exports textures. If you choose "save" in any modelling program, it will save it as a .blend file (in blender's case) or a maya ASCII file in case you use maya. That means you have to use the "Export" option.
EDIT: Ninja'd by Smoke