You'll want to look into using STYLE and SYMBOL definitions in your map file.
Here's an example of a layer with red circles for points that are 3
pixels large.
LAYER
NAME "points"
TYPE POINT
STATUS DEFAULT
DATA "points"
CLASS
STYLE
SYMBOL 'circle'
COLOR 255 0 0
SIZE 3
END
END
END
SYMBOL
NAME 'circle'
TYPE ELLIPSE
POINTS
1 1
END
FILLED TRUE
END