When you open a file that contains textures, you may either get a folder of textures or a single texture.
Editing these is fairly simple.
You can export the texture by right clicking it and selecting export.
Then select the format you want. I suggest using .png as it is supported in most image editors.
Use any image editor and edit your image or you can use another image instead.
Right click your texture and click replace.
Select the image you want to replace with.
If you are not using DDS, you will get a settings window. These default settings are fine.
Click "Ok" and now you are done.
Now save with File - Save / Save As or with CTRL + S
Tips
Default Program Editing
This setting can be used to automatically open an image in your default image editor. Simply select your formats and "Edit Default Program" if necessary.
Saving back this dialog will show. Select "Ok".
Editor Orientation
You can adjust the orientation of the properties panel.
Gamma Correction
Enable gamma correction previewing to fix dark textures often found in Smash Ult.
Fill Blank Color
Edit - Fill Color can automatically fill in colors.
They can fill normal maps too!
Channel Swapping
Channels can be viewed in the channels tab.
Channels can be swapped in the properties window.
Note these settings are limited to only certain formats that have these properties!
Here I made the green channel used for alpha/transparency and red for the rest (RGB).
Alpha Hide
This is only for preview. The alpha channel can be hidden to see the raw RGB view.
Cube Maps
Cubemaps can be viewed in View - Preview Cubemap.
Alpha can be turned off if the map does not show well (transparency can be used for other effects like intensity).
They can also be viewed in 3D view.
