Many years ago I did machine quilting for extra income. I would move the frames with the the quilt under the needle and make the designs. So I am curious, how does a free-arm machine work? Are the designs freehand or what?

Not sure what you mean by a free arm machine. Did you mean to say longarm machine?

Yes, I meant long arm. Sorry.

with a long arm=
the quilt backing/batting/top are loaded on a frame-the machine rides on a carriage which in turn is on tracks-
you take ahold of the handle bars and (drive) the machine over the surface of the quilt.
there are TONS of machine quilting videos---or visit a long arm dealership to see it in action-
a couple with good web content are:
gammil
Handiquilter
Nolting
APQS

there are more- those are just a few off the top of my head-
visit their websites- and watch a quilt get quilted.