This article is from the Miniatures Painting FAQ, by Brenda Klein firstname.lastname@example.org with numerous contributions by others.
Get the smallest file you can find, a pair of scissors, and
some glue. If it's a plastic miniature, you can use model
cement or super glue, if it's metal use Zap-A-Gap, super
glue, or any model formulated cryanoacrylate. On plastic,
first clip in as close as possible with scissors (nail scissors
are excellent) then file. On metal, carefully file the edges.
The goal is to get the pieces to fit together as closely as
possible. Once they do, clean them with soap and water to
remove all shavings, dry, and glue. Hold for about twice as
long as is recommended for the glue to set. The innovative
miniaturist can come up with a great many ways to clamp,
fasten, or hold parts together until everything's dry.
(Regretfully, the author has forgotten who posted this
tip [likely it was Tom Harris], but it's excellent:
"A little note, if you're working with super glue keep
a wet teabag handy. If you spill super glue on your
hands wipe it on the teabag and the teabag will absorb
it - teabags are highly absorbant of chemicals. It works
great for me and I don't end up with shells on the ends
of my fingers of dried super glue.")
(This one comes from John F. Bailey <email@example.com>:
"If you do become adhered to yourself or pieces via
superglue (cyanoacrylate), most of them can be dissolved
with acetone. May take a little soaking, but it works.
Unfortunately it also removes skin oils almost completely.
Follow it with isopropyl alcohol to neutralize the acetone
then lots of soap and water to neutralize the alcohol, and
then a good moisturizing lotion to replenish skin oils and
avoid those nasty dry skin diseases (eczema, etc.). A bit
of a pain, and it eats most plastics, but a whole lot
better than surgery to remove that battle-axe. A
preventive technique is to use "barrier creme", not a lot
of mechanics in this country use it even though it is very
common in the UK, but I have obtained it by asking for it
in pharmacies/drug stores. You put it on like hand lotion
before you get into something. It dries to a thin film
that protects your skin from most solvents, gas, oil,
etc., and washes off with soap and water.")
Note: If working with cryanoacrylate, have the acetone (nail
polish remover is the most available form) on hand and nearby.
When you aren't prepared, you'll end up stuck to something.
Murphy loves modellers.
Once the glue has dried, take an X-acto blade or razor blade
and carefully clean off the excess glue, if any. A file or
emery board will also do the trick.
You'll have to wash the miniature again before primering, to
remove hand oils and glue remains.
After you've gotten the basics of gluing your miniatures,
the best stuff you can use is epoxy. It's permanent, filable,
and works exceptionally well on miniatures that will get a
lot of handling.