Draw a line segment of arbitrary length.



Open your compass to the same length as the segment.
Put the sharp point of your compass on the LEFT end
of the line segment, and swing an arc like this.



Without changing your compass, put the sharp point 
of your compass on the RIGHT end of the line segment, 
and swing an arc that intersects the first arc. Like
this:



Draw a line segment from the left end of the first
segment to the point where those two arcs intersect.
Like this:



Without changing your compass, put the sharp point 
of your compass on the point where those two arcs 
intersect.  Swing another arc over to the right,
like this:


 
Without changing your compass, put the sharp point 
of your compass back on the RIGHT end of the FIRST 
line segment, and swing an arc that intersects the 
last arc that you drew. Like this:



Draw the other two sides of the rhombus, like this:



Edwin