Guitar powered LED's

Projects General Guidance
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You will need an amplifier between the guitar pickup and the Arduino.

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HakuMasente:
increase brightness with volume, and change colors depending on frequency range.

That kind of light display is generally called a "color organ". A quick Google search for 'Arduino color organ' turns up several designs. Most use the MSGEQ7 chip to do the audio band filtering. You'll want to implement something like one of those designs and replace the microphone with a guitar input.

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An apparatus that takes in a 1/4 inch guitar input directly (not using a microphone to detect sound),

You might be able to get by without a preamp. You can get about one volt out of a guitar, depending on the pickup, how hard you pluck, and the guitar's volume control (and the load impedance).

Since you can't feed negative voltages into the Arduino, you'll need to [u]bias[/u] the Arduino's input at 2.5V. And since a guitar wants to see a high impedance load, I'd suggest using 2 megohm resistors (assuming you don't add a preamp).

and following specifications in my code, adjust a strip of LED's to increase brightness with volume, and change colors depending on frequency range.

Search for "Arduino Spectrum Analyzer".

This can be done in software, but the [u]MSGEQ7[/u] is a slick solution if 7 frequency bands is OK for you. The MSGEQ7 also takes care of the offset/bias problem for you.

BTW - The guitar won't be "powering" the LEDs, it will be "controlling" the LEDs and the power will come from a power supply or battery.

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I'm not the OP but I'm enthused because my 2 hobbies are guitar and Arduino. DVDdoug, that MSGEQ7 looks fantastic, thanks for suggesting it. It lets you offload a huge amount of tedious software and hardware work to a little tiny DIP chip. Looking at example sketches and how few hardware parts would be needed for this, it looks way easier than I originally thought when I started watching this thread.

This stereo shield is out of stock, but the schematic and hookup guide is available: SparkFun Spectrum Shield - DEV-13116 - SparkFun Electronics
Another interesting site:
http://tronixstuff.com/2013/01/31/tutorial-arduino-and-the-msgeq7-spectrum-analyzer/
OMG the project is damn near done for me before I even start, I'm going to beat the OP to completing his own project:
http://www.ebay.com/itm/MSGEQ7-Breakout-Board-Arduino-microprocessor-/321746523983