Animate the Opacity of all items in the comp from 100 (or whatever) to zero. Render in a codec that supports Alpha Channels.
Black is the standard background for media players and the only place you will be able to actually see a transparent background is in an editing app that supports alpha channels. If you have no solid layer at the bottom of your timeline, which you can verify by activating the transparency grid in the composition panel, and you render to a format that supports all the channels your rendered video will fade to transparent.
One of the formats that supports transparency (Alpha channels) is JPEG 2000 in a QuickTime container. The output module in the render cue has a preset for lossless with Alpha. You can use that one. Unfortunately the default in the output module for rendering alpha channels (RGB + Alpha) is pre-multiplied and for 99.99997% of applications this is wrong. Alpha channels should be rendered "Straight" and less you absolutely positively know exactly what you're doing.
I hope that answers your questions.