Once you know the name of a texture used in the original Morrowind, you can just put a texture file of the same name into your "Morrowind\Data Files\Textures" folder and Morrowind will automatically use the new texture instead of the one from the original game.
The game's texture files can all be found on the Construction Set CD if you want to edit one.
If you
don't know the name of the texture you want to edit, but you know which model uses that texture (for instance, you don't know the name of a particular Hlaalu texture but you know that it's used by a certain model), you can find out the name of the texture by opening up the model in a program like NifSkope.
If you don't know the name of the
model either, you can open up the Construction Set and find the object that you're looking for; double-click on it, and it will say what model it uses. Then you can find the model, and then you can find the texture
Sorry, not exactly "hefty" guidance but hopefully it will give you an idea of what you need to do. Once you know the name of the texture you want to replace it's actually very simple