I have used a commercial video editor before, but with blender’s sequencer, I rate as a newbie. It is not obvious to me how to fade in from black at the beginning or fade out to black at the end of a strip of video. The VSE Manual
Animate the strip’s Fac parameter in the IPO editor as follows:
Select the strip.
In the IPO editor, open the rollout menu and select IPO Type: Sequence.
The only parameter available will be Fac (for Factor).
Control-left-click in the IPO editor window to create an IPO curve that goes from zero to 1.0 over the time you need.
Edit: Look under “Animating Audio and Video Effects” here.