Transparency (Alpha) Tween
Flash CS3 Tutorial
How to Animate Alpha in Flash
Alpha Tweening works great to fade in objects over time.
If you are fading in an object with a black or white background you might consider a Brightness Tween because it is less processor intensive. For more information, see topic Brightness Tween.
Set your background to a shade of blue (Modify > Document)(Cmd/j (PC-Ctrl/j).
Add an oval shape to the stage using the Oval tool (o key).
With the oval shape selected, convert it to a Movie Symbol (F8)(Modify > Convert to Symbol).
Click frame 20 and press F6 (Insert > Timeline > Keyframe).
Right-click the timeline between your keyframes and choose Create Motion Tween from the pull-down menu.
Click the keyframe at frame one, then click the oval object.
From Properties panel (Cmd/F3 (PC-Ctrl/F3)), select Alpha from the Color menu.
Set Alpha to 0%.
To render your swf file, press Cmd/Return (PC-Ctrl/Enter).