Step 1:
Choose the image that you want as your button. Then convert it to symbol (F8) and make sure movie clip is selected. Name it Image.
Step 2:
Select the Image Movie Clip and convert it to a movie clip again by pressing (F8). Name the movie clip "Fadein".
Step 3:
Edit the Fadein and right click on frame 15(you can replace this with another value. The more frames the smoother the transition.), then select Insert Keyframe. Right click on frame 15(or whatever frame you chose) and select motion tween. Right click again on frame 15 and select actions and input "stop()".