This article is from the Miniatures Painting FAQ, by Brenda Klein email@example.com with numerous contributions by others.
Not much. Something to hold your water/solvent (two of them if
you're working with metallics, one for the regular paint and one
for the metallic - keeps flecks out of the other stuff, and change
often to keep from muddying your colours), a palette of some sort
(professional, ceramic tile, old plate, even the plastic bubble
from a large miniature or two - Coyt suggests the plastic lid from a
large margarine tub or the like covered with foil. When done, strip
the foil off and discard), and GOOD LIGHTING. Against a window is
ideal, if not a good overhead light or adjustable lamp is a must.
Paper towels or napkins - some for blotting your brushes on and some
extras for the inevitable spill or splatter. Time - never enough of
that so learn to paint bits at a time (also good so that one layer
can dry before you put on another). Ventilation, ventilation,
VENTILATION! All paints give off noxious fumes, whether you can
smell them or not, and unless you like having headaches, you'll want
lots of space, open windows, even a fan or two.
The above are the "needed" things. Below are optional:
A magnifying glass - useful for seeing fine detail.
[A tip from Coyt D Watters which might be useful:
"I started using a magifying visor (jewelers) which gives me 2x and
flips up out of the way. Gee what a difference! Now I can easily
detail those little things like dart feathers, buttons, and laces.
My 0 brush looks about 5" around though. They are a little
expensive, but a good quality one can be purchased from Micro-Mark
for under $20. And, because it's on my head, I don't have to move
around to get a good clear view, nor is a magnifying glass in the
way of my brushes."]
An X-acto blade can be helpful, tweezers can be invaluable if
you'll be gluing, files and emery boards are used to remove sprue,
mold lines, and anything else you don't want. Nail scissors get
into places larger ones can't.
As you get more practiced you'll start finding other things to use
in your painting pursuits (such as toothpicks and small brushes),
so you'll acquire your own personal array in time.