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Edit by Edgar: I tested the OCR1A values with an oscilloscope. At the end of this answer are the frequencies.

Edit by Edgar: OCR1A values and frequencies

Value, MHz
 0 8.00
 1 4.00
 2 2.67
 3 2.00
 4 1.60
 5 1.33
 6 1.14
 7 1.00
 8 0.889
 9 0.800
10 0.727
11 0.667
12 0.615
13 0.571
14 0.533
15 0.500

you use TCR1A, COM1A0 and similar variables. Are these always present and implicitly defined when running code on the ATmega

Registers like TCCR1A and so on are defined in files which are automatically included by the Arduino IDE. If you use another toolchain they may be also automatically included. The start point is:

#define <avr/io.h>

Inside that file it checks your processor type (from a symbol passed to the compiler) and then includes an appropriate sub-file. Inside those files are defines which relate the register names to their address in the address-space of that particular chip. For example:

#define TCCR1A _SFR_MEM8(0x80)

The _SFR_MEM8 basically generates a pointer to a volatile address (because it might change without the compiler knowing it) and then dereferences that variable.

Notice that the number 0x80 in that define agrees with the number shown on my chart.

Underneath that define in the appropriate file are also the bit positions for the bits in that register, like this:

#define TCCR1A _SFR_MEM8(0x80)
#define WGM10 0
#define WGM11 1
#define COM1B0 4
#define COM1B1 5
#define COM1A0 6
#define COM1A1 7

Secondly, do I correctly understand that the output pin is defined in TCR1A, Output A and Output B, to be on Digital Pin 9 and 10 respectively?

Yes, in effect. The datasheet says that if you set the appropriate bits in TCCR1A (note the spelling) then OC1A (board pin 9 on the Uno) or OC1B (board pin 10 on the Uno) will be unchanged/toggled/cleared/set depending on the bits. You can find these names on the datasheet for the Atmega328P (and other devices) and then use the Arduino schematic to find which processor pins are connected to which board pins.

Atmega328P datasheet snippet:

Uno datasheet snippet:

Why do you set it to "Toggle" rather than "Set"?

Because every time the counter matches I want to flip the pin. That is, on/off/on/off etc.

What does CTC stand for?

Clear Timer on Compare. What this means is that (unlike other modes) once the compare match is made, the timer is cleared, thus it starts counting up from zero again.

This outputs 8 MHz on pin 9:

#ifdef __AVR_ATmega2560__
  const byte CLOCKOUT = 11;  // Mega 2560
#else
  const byte CLOCKOUT = 9;   // Uno, Duemilanove, etc.
#endif

void setup ()
  {
  // set up 8 MHz timer on CLOCKOUT (OC1A)
  pinMode (CLOCKOUT, OUTPUT); 
  // set up Timer 1
  TCCR1A = bit (COM1A0);  // toggle OC1A on Compare Match
  TCCR1B = bit (WGM12) | bit (CS10);   // CTC, no prescaling
  OCR1A =  0;       // output every cycle
  }  // end of setup

void loop ()
  {
  // whatever 
  }  // end of loop

This outputs 8 MHz on pin 9:

#ifdef __AVR_ATmega2560__
  const byte CLOCKOUT = 11;  // Mega 2560
#else
  const byte CLOCKOUT = 9;   // Uno, Duemilanove, etc.
#endif

void setup ()
  {
  // set up 8 MHz timer on CLOCKOUT (OC1A)
  pinMode (CLOCKOUT, OUTPUT); 
  // set up Timer 1
  TCCR1A = bit (COM1A0);  // toggle OC1A on Compare Match
  TCCR1B = bit (WGM12) | bit (CS10);   // CTC, no prescaling
  OCR1A =  0;       // output every cycle
  }  // end of setup

void loop ()
  {
  // whatever 
  }  // end of loop

How can add a prescaler?

You change the prescaler bits. You can look at the datasheet or my cheat sheet here:

You may not need a prescaler, depending on the frequency. Change OCR1A to some number between 0 and 65535 to slow it down.