1. Make your logo as desired. Leave the area that you desire to be transparent as one solid color. For this example, I'll be using Dragomerian Airlines' logo, since it has a nice solid black background (whatever color it is doesn't matter):
2. Upload to LunaPic. LunaPic is a free online photo editor that, among many other awesome features, allows you to choose a color in a photo and make it transparent instead.
3. Use the transparent tool. In the menu right under the LunaPic logo, hover over the "Edit" menu, and choose "Transparent" from the list.
4. Click the color that you wish to make transparent. The transparent tool allows you to select a color from the picture that you wish to replace with transparency.
5. Wao! Results! Use the save buttons right below the resulting picture to save it.