Select the object you want to make transparent. Create a rectangle and fill it with black and white gradient.
(The gradient you use as a mask doesn´t have to be black and white, you can use any color you like).
Make sure the gradient is in front of the object you are working on. And Select both objects.
If you click on the gradient icon in the Transparency panel, you can play around with the gradient on the artboard, changing the direction and position of the gradient.