I often polish by hand as sometimes it is the best way to get into
small spaces or simply get a good flat surface without putting in
more scratches than you take out.
To start, I recommend taking the piece down to at least a 1,200 grit
paper, make sure you sand in more than one direction as that allows
you to see if there are any scratches left, and using a sanding stick
(the paper wrapped around a bit of wood) will speed the process. I
then go from a medium greasy (a polishing compound, I think it
equates to about a 6000 grit paper) to High Bright (also called White
Diamond, a fast cutting compound advertised for polishing steel, its
faster and gives a better finish than tripoli) and finish with rouge.
As a backing I tend to use a rag, thread or piece of leather,
depending on the job, and will support this with a bit of wood if
required. Some turps or paint thinner (NOT nitrocellulose!), can be
used as well to help get the polishing compound onto the backing, but
this is not always necessary. It also helps to clean the piece between
changes in compound, and obviously change the backing.
Then there is elbow grease. Polishing is always a massive effort, and
by hand you really feel it. Very satisfying though.
Also a handy tip on cutting things out draw it on paper first and
then glue it to the metal. If you rough the surface of the metal up
with fine steel wool and use wood glue (PVA) then it will hold well,
it is also handy as it removes the problem of the reflection making
it difficult to follow the pattern. Purists recommend using rice
paper, but in reality standard stuff works just fine. Which means
that you can design on computer and then use the print out as a
template, opening the whole of the internet to you for inspiration
clip art is particularly good. And sit low the work piece should be
in line with your chest, it makes controlling the saw easier and is
better for your back.