1. Open the File you're using. Here's the one I'm using:

Notice on the Right side, in Channels, it only has Red, Green and Blue

2. In the Center Window (where your image is) select LAYER-> TRANSPARENCY-> ADD ALPHA CHANNEL

3. Select the areas you wish to be Transparent, using the selection tools.

4. With the ALPHA layer selected, use the ERASER tool to remove the areas you selected.

Now see how the ALPHA channel shows the black & white Alpha channel of your image?

5. Re-select the other Channels

6. In the LAYERS tab, select the Layer

7. Now Save your image. Name the image. Click on Select File By Type and chose TARGA. Make sure to un-select RLE COMPRESSION and ORIGIN AT BOTTOM LEFT. Now click on OK. Thats all there is to it!