just draw dots (point primitive in your graphics framework)
keep an array of your stars. Each star should have the following properties
position x
position y
speed x
speed y
color
at each redraw pass, add speed x and y to the position of the star, the draw it. use the color of the star
now if you keep an array of "star" structures, a simple loop through all the stars to increment the x,y position by the speed x,y will give you a nice starfield.
if you initialize your stars with different speeds and colors (especially if the color is darker when the speed is smaller) then you get a nice 2d starfield. the speed x and y will definie the direction of the motion.
So in your case, the x speed should be zero. y speed can be positive or negative to move your stars up or down