In the colour selection I have been searching for a transparent option, but I can't find one. How can I do it?
Transparency is not a color. Its a property of the image.
There are many ways by which you can induce transparency in your image.
If you want for eg all the red regions in your image to be transparent, go to Layer -> Transparency -> ColorToAlpha and select red color in the 'From' box and click OK. You will obviously need to know the exact HTML-notation of the shade that you want to turn transparent.
If you want the whole layer to be transparent, then play around with the opacity slider as Brian puts it.
Let me know if you need any other help.
NOTE : Only png and gif support transparency. If you save your transparent image as a jpg, all transparent regions would be defaulted to white as jpg doesnt support it.
If you want to make existing color (that is, pixels with a given value of transparency in your image) more transparent, you can use the Eraser tool in GIMP.
Make sure that your image and the layers you're using it on have an alpha channel, otherwise the eraser will just erase to the current background color.