You'll now need to create a simple object with a greyscale gradient. This can be accomplished in a number of ways--standard gradients, gradient meshes and blends--but for now, let's create a blend with a star-shaped object.
Choose the Star tool from the toolbar -- you'll find it in the same place as the Rectangle tool -- and create a star shape that fills most of the document. (Or, choose the Star tool and click the center of the canvas. This calls star settings window. Enter Radius 1: 800, Radius 2: 420 and Points: 5, and then click OK.)
Select the star and then choose File > Copy, followed by File > Paste in Place. This pastes a copy of the star on top of the existing star, and for the moment, it'll look as though there is still only one star on your canvas. Choose Object > Transform > Scale. A Scale window appears, allowing you to precisely scale the object you've just pasted. Click Uniform, enter 25% and then click OK. You'll see a small star sitting atop the original large one.
Now you'll need to set to colour for each star. Choose Window > Color to call up the fill and stroke colour panel. You'll see two boxes in the top left, which represent the colour of the fill (the solid square) and the stroke (the square with the square hole in it). Clicking either square brings it to the front, allowing you to change the colour of that attribute. Select the small star, bring the stroke square forward (if necessary) and then remove the stroke by clicking the white box with the red line through it, found in the bottom left of the colour panel. Now bring the fill square forward and set the fill color to a dark grey (for example, enter an RGB value of R=77, G=77, B=77).
Repeat this process for the large star, removing its stroke but this time setting the fill color to white (RGB R=255, G=255, B=255). When you click on the canvas, the large star will disappear--no need for concern.
Choose Select -> Select All, followed by Object -> Blend -> Make. Instantly, you'll see a soft gradient appear between the two stars.