There are two common types of trainers available: stationary trainers and
rollers.
Stationary trainers clamp on to your rear fork and provide a rolling
mechanism
for your rear wheel. Resistance is offered by wind (a fan attached to the
roller), fluid (a fan incased in oil attached to the roller) or magnets.
Wind
units tend to be the cheapest. Fluid resistance tends to offer the smoothest
ride. Magnetic units often have adjustable resistance. If you get a
stationary
trainer you should also get a block for the front wheel to keep the bike
level.

Stationary trainers have the following advantages/disadvantages:

Pros:
Excellent for spin/muscle/aerobic training
Easier to ride/learn
Cheaper (usually) than rollers
Some have computer interfaces to simulate road conditions
More options for resistance control
Cons:
Do nothing for balance and form
Allows you to coast
Cause a lot of wear on the rear wheel
Causes more stress to the frame of the bike
Requires no thought so can be mind numbing

Rollers provide 3 tubes two of which are connected by a belt. The front
wheel
rests on a single tube and the rear rests between two tubes. The belt from
the
front rear tube to the front tube causes the front wheel to spin with the
rear
wheel. Resistance is offered by friction and gears (smaller tubes offer more
resistance) or a fan unit attached by a belt to one of the tubes. Rollers
have
the following advantages/disadvantages:

Pros:
Excellent for spin/muscle/aerobic training as well as form and balance
Ride is more true to actual road riding
Do not allow you to coast
Force you to concentrate on your workout
Less stress/wear on bike


Cons:
Harder to learn/use
More expensive than basic stationary trainers
Less resistance options

The big reason most people avoid rollers is that they have a steep learning
curve. The common fear is that you will ride off the rollers and hurt
yourself.
You can't actually ride off rollers like you might imagine, the only thing
you
can do is drop the front wheel off of the side of the roller which can cause
you
to loose your balance and fall. The best tip for learning to ride rollers is
to
start in a doorway so if you loose your balance you can just stick out your
elbow to stop your fall.