Step By Step
Step 1: Choose your program to edit with This could be Photo Shop (not free), Paint Shop Pro (free trial), Irfanview (free, but no image creation), or The Gimp (free and full featured image editing) just to name a few.
Here Photoshop is being used:

Step 2: Open the image you wish to edit, I chose the main image from my skin A.K.A Main_Image.tga
Note: All the files you will be editing have the extension .tga
Note2: You DO NOT have to edit the default valve and steam logo files, you can create your own files, and save them as blabla.tga (where blablah is what you want your file called).
Note3: For your Icons it will help you edit the ones that steam comes with, they can be found in the \Steam\Skins\Grey\Resource\ folder and should be copied to your \Steam\Skins\SkinName\Resource\ folder and editedinstead

Step 3:Edit the image, if you don't know how to do this, then I would suggest NOT skinning

Saving your Images
2 Programs discussed will be PS, and Irfanview
Photoshop:
This should be fairly simple. Do not reduce your palatte at all after, make sure your in full RGB mode by going to Image > Mode > RGB. If you're good there then go to File > Save As on the top of your screen

After clicking Save As... a prompt will come up, asking you to save the file. Make sure it is in the correct path, the file name is correct, it might change to Valve_Logo_copy (if you are using the original image), and that the file is being saved as a Targa, it will automatically save as .tga if Targa is selected.

If you are not using the original image, skip this step
After clicking Save, a prompt will come up, asking if you wish to overwrite it, click yes, but be aware, once you save it, you recover the old image.

Now is the most important part, a new prompt will come up, asking for the Targa options, choose 24 bits/pixel The images are only visibly at 24 bits/pixel... 16 or 32 will NOT work

Irvanview:
This should be even easier than with photoshop... You can't create files but you can easily convert existing ones to .tga format Open the file you want to convert, then go to File > Save As on the top of your screen

After clicking Save As... a prompt will come up, asking you to save the file. Make sure it is in the correct path, the file name is correct, it might change to Valve_Logo_copy, and that the file is being saved as TGA Truevision Targa.