Teto

Start by creating a new image. Go to "File->New..." or click Ctrl+N, you'll see this dialog:

Name the image whatever you like, it's not important. Set the width and height to 128 for our example. Make sure the units are in pixels, and resolution is 72 pixels/inch. Before you click OK, make sure "Transparent" in the "Contents" area is selected. This will make our image transparent as default and is important when making the alpha channel.

Click "OK".

You'll see your empty workspace. Note the checkered appearance, this indicates the background is transparent.

Now, select a brush that is nice and fuzzy, I used 17px sized fuzzy brush.

Draw a nice smiley face. I made mine happy :-) I like happy... Happy is good my brother said.

See the small representation of our smiley? Right click the image and select "Select Layer Transparency".

NB! You must click on the actual icon. If you click the text in the blue area (where it says "Layer 1" in the image) you will get a different menu with other options.

NB! NB! Here is why we chose a transparent background. This point had me illuded for quite some time because I thought Photoshop would use this as the alpha channel, which apparently was not the case.

Tip: If you have multiple layers here and want a general alpha channel, select the entire image ("Select->Select All" or Ctrl+A), and copy merged ("Edit->Copy Merged" or "Shift+Ctrl+C"), create a new image and paste it in. Now continue with the following steps.

Click the "Channels" tab (it's next to the "Layers" tab in the same window). 

Down at the bottom there's an icon to the left of the trashcan that looks like a notepad with a page flipping over. I've marked it in read so it's easier to spot. Click this, it will add an alpha channel. Now, select the bright white color and use the "Fill" feature ("Edit->Fill" or "Alt+E" then "L"). This will fill the selected area with white. Since we had selected the layer transparency, this will create a perfect alpha channel for our image :-)

You should now be seeing this black and white representation of our image and we can save our image with an alpha channel.

Edit:

I forgot to mention that the transparent background in Photoshop will be saved as white, and this will show through. To prevent this, there's a nice feature called "Flatten Image". Go to "Layer->Flatten Image" ("Alt+L" then "f"). Notice how the checkered background becomes white and the area where you have drawn something expands a little. Now things should look alright :-)

Go to "File->Save As...", choose "Targa (*.TGA;(...)" as our Format. Notice the "Alpha Channels" under "Save Options" is now checked. Click "Save" and make sure "32 bits/pixel" is selected in the "Targa Options" dialog that appears next.

Click "OK".

The image should now be saved with an alpha channel. No more ugly edges, yay! :-)