There are at least five different sorts of smoke/fog/mist used in
theatre

Pyrotechnics
These are the only way of producing a truly coloured smoke. The dyes
used will mark scenery or drapes nearby. Pyroflash cartridges produce a
jet of deeply coloured dense smoke for seven or thirty seconds when
fired, and I think Stage FX pods produce smoke for about twenty seconds.
Flashpots, gerbs and any other pyro effect will produce a lot of white
smoke in addition to the main effect. All pyro safety precautions must
be observed, See the FAQ entry for pyrotechnics for more information.

Smoke guns
Smoke guns feed a liquid ('smoke juice') into a heated chamber. It
vaporizes and produces a jet of dense white smoke.

Cheap smoke machines tend to use a pressurised canister of juice, whilst
the more expensive ones use an electric pump to feed juice from an
external tank into the chamber. The electrically pumped machines tend to
give a lot more control, and the juice is a lot cheaper than the
pressurised canisters. Pressurised canister machines can be plugged in
for a while to get the block hot, then can be unplugged and moved around
the stage and still work. (There is one rechargable pumped gun that can
be used cordless, the Scottie)

The smoke will hang in the air for a time, depending on the ventilation
of the building and the formula of smoke juice used (clubs generally use
economical long lifetime smoke juice, whilst theatres tend to use short
lifetime juice for more control).

The dense jet of smoke is a bit obvious in some contexts. One answer is
to deliver the smoke through flexible ducting. Most (all?) machines have
an adapter available that makes it easy to connect ducting to the
machine. You can buy expensive black flexible ducting from the smoke gun
supplier or use cheaper tumble-dryer exhaust ducting.

Another approach is to control the output of the gun. Most pumped guns
have a control that lets you dribble smoke out of the gun at varying
rates. One or two (aimed at the club market, presumably) have optical
sensors available to maintain a constant density of smoke in a space.

Smoke from a smoke gun can't be coloured, but the dense white smoke
takes colour from lighting well.

Haze fluid is available for some smoke guns. This produces a very pale
smoke, quite unlike the normal dense smoke. It's not as obvious as
normal smoke, until you shine light through it. It's nowhere near as
good as cracked-oil haze, but you can use it for some of the same
effects for a fraction of the price.

Don't try and make your own smoke juice or your own smoke machine. Don't
try and use a garden fogger as a smoke gun. Don't use smoke juice in a
machine it isn't recommended for. Using the wrong block temperature/fog
juice combination can produce irritant, carcinogenic or toxic gasses.

Flavoured smoke juice is available, often at a discount over normal
juice. Don't use it. If the cast don't lynch you your crew will. Pina
Colada smoke juice is particularly nasty.

Allergic reactions.
Some actors will believe that smoke will cause them to cough (as will
the audience). In my experience this is pretty much psychological.
Newbie actors will choke for a while, but people who've worked with
smoke before won't notice it. Ensure your cast get a chance to rehearse
with smoke before the dress. Smoke will dry the throats of singers or
woodwind/brass players and should be avoided or minimised if you can.

Smoke chillers.
If you chill smoke using solid CO2 you can produce a low-lying smoke.
It's not as low to the floor as CO2 smoke, and will drift up as people
move. It's a very nice effect, particularly for nighttime marsh or docks
scenes. Not bad for 'victorian london' too. I've never used a commercial
chiller but have had very good results with homemade chillers, made from
a large box with an inlet at one end, an outlet at the other and baffles
inbetween. Shelves made of wire mesh hold the dry-ice that chills the
smoke. I've seen people pack smoke ducting with dry-ice for this effect,
but it doesn't work as well.

Dry-ice or CO2
A dry-ice smoke kettle is a sealed plastic box with electric heating
elements in the bottom, and a metal basket that can be raised or lowered
(think deep-fat dryer). The lower half is filled with water; brought to
near boiling by the electric elements. The basket is filled with
dry-ice. When the smoke is needed the basket is lowered into the hot
water. The dry-ice sublimes and produces a very dense white water-vapour
smoke. This is forced out of a nozzle on the front of the kettle.

These consume a lot of power, 7 or 8 kW for a medium sized kettle.

Dry-ice smoke is very dense and low-lying.

'Jekyll and Hyde' effects can be produced by dropping dry-ice pellets
into a beaker of hot water.

Dry-ice can be bought cheaply from frozen food distributors, or
'borrowed' from university physics departments. It can be stored in a
polystyrene box or coolbox for 2-4 days. Make sure that the coolbox
isn't airtight - the CO2 buildup can blow the lid off.

Liquid nitrogen foggers

Liquid nitrogen smoke machines work by spraying a fine mist of liquid
nitrogen. This drops the temperature of the air and causes atmospheric
moisture to condense into a low lying, natural looking fog

LN2 fog is common at fixed installations, such as theme parks, but can
be useful on stage.

Interesting Products answer some LN2 fogger questions at
http://www.interesting-products.com/linkpg.htm

Cracked-oil foggers
These produce a nearly transparent haze that scatters light well. Beams
of light are clearly visible in the haze, but the haze itself isn't
visible. A beautiful effect, but I've never been able to afford to rent
one.