user10884: I have put together a breadboard version of the arduino by following the tutorial on arduino's main website https://www.arduino.cc/en/Main/Standalone.
I have done everything exactly how that tutorial explains it and have double checked my work to ensure I didn't mess up a connection somehow. I have a usb mini breadout board that I am connecting from the breadboard to my computer and the pin outs are as follows:

GND -> Breadboard GND
5v -> Breadboard + rail
TXO -> IC pin 2
RXI -> IC pin 3
GND (GRN) -> IC pin 1 through .1μF cap

When I go to the arduino IDE and select the arduino duemilanove setting and upload a sketch I come out with this error: 
avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding

I am using a pre-bootloaded atmega328 chip and have switched it out with two others to make sure it wasn't the switch, but that didn't help either. 
Any ideas on what might be the problem?

user10904: 
Make sure you have a 16Mhz crystal attached to your board at the XTAL locations properly.
If you dont have one already, connect a 0.1uf capacitor (ceramic or metal film) to the reset pin for auto reset capabilities.
The avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00 issue is probably due to reset problems, where the arduino is not communicating to the computer. However, there are other possible reasons for this error. http://forum.arduino.cc/index.php?topic=28223.0
Double check that TX on the arduino is connected to Rx on the computer and Rx on the arduino is connected to Tx on the computer

If problems keep persisting, post more information so we can help you more.

user612: To expand upon what was previously mentioned in comments, there are a number of things that need to be done before you can program an ATmega via a serial  connection:

you need to have a bootloader flashed on the chip
you need to provide a clock source (internal or external) matching the fuse settings and the rate expected by the bootloader
your programming software must use the same baud rate as the bootloader is expecting
you need to have reset the chip recently enough before starting the upload that the bootloader has not timed out - either manually or via a small capacitor to your logic level serial connection's DTR or RTS line

You commented that your chip came from Sparkfun and was sold as having a bootloader.  The programmed ATmega328p's they list claim to have the Uno's bootloader, so most likely these need to be programmed at 115200 baud like an Uno.  You instead said that you had selected the Duemilanove setting, which would mean you were trying to use a baud rate of 57600.

10884: <p>I have put together a breadboard version of the arduino by following the tutorial on arduino's main website <a href="https://www.arduino.cc/en/Main/Standalone" rel="nofollow">https://www.arduino.cc/en/Main/Standalone</a>.</p>

<p>I have done everything exactly how that tutorial explains it and have double checked my work to ensure I didn't mess up a connection somehow. I have a usb mini breadout board that I am connecting from the breadboard to my computer and the pin outs are as follows:</p>

<ul>
<li>GND -> Breadboard GND</li>
<li>5v -> Breadboard + rail</li>
<li>TXO -> IC pin 2</li>
<li>RXI -> IC pin 3</li>
<li>GND (GRN) -> IC pin 1 through .1μF cap</li>
</ul>

<p>When I go to the arduino IDE and select the arduino duemilanove setting and upload a sketch I come out with this error: </p>

<pre><code>avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
avrdude: stk500_recv(): programmer is not responding
</code></pre>

<p>I am using a pre-bootloaded atmega328 chip and have switched it out with two others to make sure it wasn't the switch, but that didn't help either. </p>

<p>Any ideas on what might be the problem?</p>
 10904: <ol>
<li><p>Make sure you have a 16Mhz crystal attached to your board at the XTAL locations properly.</p></li>
<li><p>If you dont have one already, connect a 0.1uf capacitor (ceramic or metal film) to the reset pin for auto reset capabilities.</p></li>
<li><p>The <code>avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00</code> issue is probably due to reset problems, where the arduino is not communicating to the computer. However, there are other possible reasons for this error. <a href="http://forum.arduino.cc/index.php?topic=28223.0" rel="nofollow">http://forum.arduino.cc/index.php?topic=28223.0</a></p></li>
<li><p>Double check that TX on the arduino is connected to Rx on the computer and Rx on the arduino is connected to Tx on the computer</p></li>
</ol>

<p>If problems keep persisting, post more information so we can help you more.</p>
 612: <p>To expand upon what was previously mentioned in comments, there are a number of things that need to be done before you can program an ATmega via a serial  connection:</p>

<ul>
<li><p>you need to have a bootloader flashed on the chip</p></li>
<li><p>you need to provide a clock source (internal or external) matching the fuse settings and the rate expected by the bootloader</p></li>
<li><p>your programming software must use the same baud rate as the bootloader is expecting</p></li>
<li><p>you need to have reset the chip recently enough before starting the upload that the bootloader has not timed out - either manually or via a small capacitor to your logic level serial connection's DTR or RTS line</p></li>
</ul>

<p>You commented that your chip came from Sparkfun and was sold as having a bootloader.  The programmed ATmega328p's they list claim to have the Uno's bootloader, so most likely these need to be programmed at 115200 baud like an Uno.  You instead said that you had selected the Duemilanove setting, which would mean you were trying to use a baud rate of 57600.</p>
