user17022: How do I connect a function generator that generates an analog signal to an Arduino Uno?
I don't know how to begin, so could you also tell me the settings for the function generator, e.g. its amplitude, frequency, etc, that won't damage my Arduino?
I plan to visualize the output on Processing.

(source: sonoma.edu)

user13432: 
I don't know how to begin, so could you also tell me the settings for the function generator, e.g. its amplitude, frequency, etc, that won't damage my Arduino?

That is not an Arduino question. That is a question about how to operate the function generator. Please check the users manual. You need to set the voltage output (DC + AC) so that it matches the Arduino.
An analog signal should go to an analog pin on the Arduino (not pin 8). It is also important to connect GND. 
Cheers!

user10794: Confirm with an oscilloscope
When I connect my function generator I usually always make sure that the output is in the range 0 to 5V, with my oscilloscope. The default is probably more like ±2.5V - but I don't have an Agilent so you would have to check. Press the Ampl button to check. (Mine reads 5VPP). 

You can see from the above image that we indeed have (roughly) 5VPP - and that there is a -2.56V component, which will damage the Arduino, being negative.

Add an offset
So press the Offset button and add a 2.5V DC offset. Now the voltage jumps 2.5V and is between 0 and 5V:

The scope confirms that the minimum is 80mV and the maximum is 4.96V, which is in range for an Arduino pin (assuming you are running an Arduino at 5V, which is not always the case).
Now you should be safe to experiment with different frequencies and wave-forms. Just leave the Amplitude and Offset alone. :)

Extra precautions
You could feed the function generator through an input protection circuit, just in case you absent mindedly forget to carry out the appropriate steps.

The zener diode will conduct negative voltages to ground (dissipated through the 1k resistor) and will also limit positive voltages to around 5.1V.

17022: <p>How do I connect a function generator that generates an analog signal to an Arduino Uno?</p>
<p>I don't know how to begin, so could you also tell me the settings for the function generator, e.g. its amplitude, frequency, etc, that won't damage my Arduino?</p>
<p>I plan to visualize the output on Processing.</p>
<p><a href="https://i.stack.imgur.com/vi4dQ.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/vi4dQ.jpg" alt="Agilent 33220A Function Generator" /></a><br />
<sub>(source: <a href="https://www.sonoma.edu/users/m/marivani/es110/images/fg_big.jpg" rel="nofollow noreferrer">sonoma.edu</a>)</sub></p>
 13432: <blockquote>
  <p>I don't know how to begin, so could you also tell me the settings for the function generator, e.g. its amplitude, frequency, etc, that won't damage my Arduino?</p>
</blockquote>

<p>That is not an Arduino question. That is a question about how to operate the function generator. Please check the users manual. You need to set the voltage output (DC + AC) so that it matches the Arduino.</p>

<p>An analog signal should go to an analog pin on the Arduino (not pin 8). It is also important to connect GND. </p>

<p>Cheers!</p>
 10794: <h2>Confirm with an oscilloscope</h2>

<p>When I connect my function generator I <s>usually</s> always make sure that the output is in the range 0 to 5V, with my oscilloscope. The default is probably more like ±2.5V - but I don't have an Agilent so you would have to check. Press the <code>Ampl</code> button to check. (Mine reads 5V<sub>PP</sub>). </p>

<p><a href="https://i.stack.imgur.com/Jn5AO.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Jn5AO.png" alt="Default operation"></a></p>

<p>You can see from the above image that we indeed have (roughly) 5V<sub>PP</sub> - and that there is a -2.56V component, which will damage the Arduino, being negative.</p>

<hr>

<h2>Add an offset</h2>

<p>So press the <code>Offset</code> button and add a 2.5V DC offset. Now the voltage jumps 2.5V and is between 0 and 5V:</p>

<p><a href="https://i.stack.imgur.com/kk2e1.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/kk2e1.png" alt="With 2.5V offset"></a></p>

<p>The scope confirms that the minimum is 80mV and the maximum is 4.96V, which is in range for an Arduino pin (assuming you are running an Arduino at 5V, which is not always the case).</p>

<p>Now you should be safe to experiment with different frequencies and wave-forms. Just leave the Amplitude and Offset alone. :)</p>

<hr>

<h2>Extra precautions</h2>

<p>You could feed the function generator through an input protection circuit, just in case you absent mindedly forget to carry out the appropriate steps.</p>

<p><a href="https://i.stack.imgur.com/Pm0WV.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Pm0WV.png" alt="Input protection"></a></p>

<p>The zener diode will conduct negative voltages to ground (dissipated through the 1k resistor) and will also limit positive voltages to around 5.1V.</p>
