There are two ways of looking at this:

The first way of approaching this topic is from the physical characteristics of the
radio. In this case there are two types of radios. The most common is a ‘pistol
grip’ type radio. This is the type that you hold in one hand, kinda like a hand
gun. On your trigger finger you have a lever that controls the speed: the throttle,
with the other hand you hold on to a little wheel that controls the direction of
the car: the steering. These radios mostly come in right hand configuration - you
hold the radio in your left hand, and steer with the right - left handed radios are
also available, but there are fewer to chose from. The second type is a ’stick’ or
‘paddle’ type. This type of radio you generally hold with both hands, and with your
index finger or thumb you hold on to two levers sticking out of the top. One level
is the throttle and the other is the steering. The stick type of radio, in car
racing, is decreasing in popularity in favor of the pistol grip, but there are
still few around.
There is apparently a single-stick radio out there. This works similarly to a
joystick. I have never seen one, I am only spreading the rumor … If anyone has an
URL to a manufacturer, please send it my way.

The second way of looking at this topic is the type of communication, the radio
uses. I will, unfortunately, have to use some electronics terminology to be able to
describe this. The radio transmits a radio signal which is picked up by a receiver
in the car. So that more than one person would be able to race their car at the
same time, each radio is assigned a particular frequency - this frequency is
referred to as the ‘carrier frequency’. Out of convenience, each carrier frequency
is assigned a ‘channel number’ (see “Legal frequency - channel tables” at the end
of this document). Almost all radios today can have their channel changed by
changing a ‘crystal’ in the radio - this is a small electronic device which
generates the appropriate carrier frequency. The radios are intentionally
manufactured to make this relatively easy to do. The receiver must have a matching
frequency crystal as well. Normally people get multiple crystal sets, so that when
they get together with friends or for a race there is less likelihood that several
people will have the same channel. In fact, if you enter into a race they will
require you to submit three channels that you can race on, and just before your
race they will tell you which of your three you must use.
There are different methods to generate the carrier frequency, this is called
‘frequency modulation’. There are three types of modulation that you will see when
shopping for a radio. AM - Amplitude Modulation - is the simplest, least expensive
method of signal transmission. The next type if FM - Frequency Modulation - which
has inherently slightly better range and is less susceptible to radio interference.
The last type is PCM - Pulse-Coded Modulation - which is a type of AM or FM
modulation, but it has a greater range and resolution. PCM signals are coded in
such a way that interference is almost nonexistent.
8.1. What is all this stuff on the radio?

When you drive your car, the radio will impress information onto the carrier wave.
The type of information that is impressed onto the carrier is: going left / right
and how far to the left / right, go forward / backwards and how fast forward /
backwards. Unfortunately, each of these functions is also referred to as a
‘channel’. So a radio that can control steering and speed will be a 2-chanel radio.
These channels are different than the channels for the carrier frequency; it is
just a confusingly similar label. The receiver in the car then decodes this
information, and generates appropriate electrical signals for the devices that are
connected to it: the steering servo and the speed controller. These devices then
transform those signals into the physical: your car moves! The term ‘proportional
radio’, which might pop up while you’re shopping, means that as you press more on
the throttle the car moves proportionally faster; same goes for the steering. This
is opposed to simple on-off control: the car is either standing still or going full
blast - most toy R/C cars use on-off radio control. Check
<http://www.howstuffworks.com/rc-toy3.htm> for a different explanation of the same
thing, and with pictures. 
All of this is quite simplified here. If you want more (technical) detail you can
look up how a radio works in any electronics communications textbook.

The method used to generate the radio signal (the modulation) is pretty
standardized. The way to impress the information onto that carrier signal is
different for each manufacturer. This means that radio made by company A will
probably not work with a receiver made by company B, even if you have matching
frequency crystals. The whole set: radio, receiver, and crystal set come as a
matched set. There are third party manufacturers that make receivers that are
compatible with first party manufacturers. Check with the manufacturer of your
equipment before you commit to a purchase!
One thing worthy of note is that crystals (channels) are interchangeable between AM
and FM radios made by the same manufacturer. However, the radios are built so that
crystals are not interchangeable between manufacturers - you need to buy crystals
made for your brand of radio.

There is also something called a ’synthesized frequency module’. This is referred
to differently by different manufactures, for example: ’spectra module’,
’synthesized transmitter’, etc. The idea is rather simple (to the end-user anyway).
There is an extra piece of electronic built into the radio that will allow you to
dial in the desired frequency: no more crystals to swap. You can (but do not have
to) get a receiver with the same thing in it.

Another feature is something called Battery Elimination Circuit - BEC. Normally you
need a battery pack connected to the speed controller which drives the motor, you
also need a separate battery pack to power the receiver itself. Most receivers
today have a BEC, which eliminates the need for the battery pack going to the
receiver. The receiver gets its power from the motor battery pack. Less weight for
your car to carry, less run time though; the tradeoff is worth it however.

8.2. Radio interference

There is a whole bunch of stuff that can cause radio interference. How you detect
it is very simple: your car goes crazy. If interference is a problem for you, go
through the following list and see if you can eliminate any of these. I tried to
put suggestions as to what you could do to fix the problem; some of these are
simple and inexpensive, while some others …
 - As stated before, from most to least susceptible types of radio transmission:
AM, FM, PCM. The less susceptible you get, the more it will cost you.
 - Some people experienced a lot of interference when standing close to their car,
especially with AM radios. This is especially a concern for nitro cars, when
starting their car up.
 - Some people claim that the 27MHz band is more susceptible than the 75MHz band
(in the US). The reasoning here is that the 27MHz band has the channels spaced
further apart, this leaves more room for error. R/C toy manufacturers, who are not
very concerned about making quality equipment, take advantage of that.
Unfortunately, you cannot simply change the crystals to the 75MHz band - you would
need to get a whole new radio.
 - Sparking (arcing) coming from the motor. Get new brushes; clean your motor;
install noise capacitors on your motor: check the manuals that came with BOTH your
motor and your ESC on how to do this correctly.
 - Bad (bad = old, defective, or possibly cheap) servos.
 - People standing next to you are using channels that are next (or close) to
yours. Change your channel.

8.3. Using a 4-channel (or more) radio with a car

Most radios used for R/C cars are 2-channel: direction and speed. There are also
3-channel radios; the third channel is used for fancy stuff. For example, some
people wire up lights on their car to the third channel. Higher number of channels
(up to  is intended for aircraft, but can it be used for cars?

This will work, but there are a few things you must keep in mind. Different radios
are designed for different applications. You might have to use some trial and error
to figure out which channel you want to use for the throttle and which for the
steering on your car. Also, multi-channel radios are intended for airplanes and
other flying R/C models. The throttle for a car radio is spring loaded, but for an
airplane it is not. This means that on a car radio when you let go of the throttle,
it will return to the neutral position. On an airplane radio the throttle will
stay, by design, wherever you had pushed it to. It will require some getting used
to, but it can be done.

Yes, there are also legal issues as well! You must use the correct frequency for
your radio. Certain frequencies are reserved for air use only, and some others are
for ground use only. At the end of this document, see “Legal frequency - channel
tables”, there is a list of legal frequencies for ground vehicles only.
I personally am no lawyer, and as such I am not familiar with all the legal
subtleties! In North America the government authority responsible for this is the
FCC - Federal Communication Commission - which controls everything transmitted
trough the air. They have a web site, and the relevant pages can be found at:
<http://www.fcc.gov/wtb/prs/radcntrl.html>, and
<http://www.access.gpo.gov/nara/cfr/waisidx_00/47cfrv5_00.html>. In the UK it is
The Radiocommunications Agency; here is the best link I have been able to find:
<http://www.radio.gov.uk/publication/ra_info/ra60.htm>. Good luck!

8.4. Too much information on radios

Someone posted a message asking for plans to build his own radio. This topic is way
too advanced for the scope of this FAQ. However, Rudie Shepherd provided the
original poster with some very excellent URLs to sites with this type of
information. For those truly into way too much information, here are the links:
MicroPro8000 Users <http://mp8000.rcclubs.com/>
Radio Modelisme (in French and English) <http://home.nordnet.fr/~fthobois/>
RCMICRO: Microprocessor based radio control encoder
<http://www.eagleairaust.com.au/encoder.htm>

Here are a few more links describing how to build your own electronics, or modify
your electronics. Please note that modifying your equipment will most certainly
void the warranty on your equipment. 
The 7 channel hack: <http://www.teamtornado.co.uk/7channel.htm>
PC-to-R/C Interface: <http://www.mh.ttu.ee/risto/rc/electronics/pctorc.htm>
Micron Radio Control: <http://www.micronradiocontrol.fsnet.co.uk/>