There are many, many scenarios here, but I will cover a couple of basic ones to get you started. When recording an acoustic guitar, you in essence three options. I'll enumerate those, and then go through some basic questions to hopefully get you moving.
- Use an Acoustic/Electric guitar and plug it into a recording interface of some kind.
- Mike an Acoustic guitar without any electronics and plug the mike into a recording interface.
- Install a pickup into an Acoustic guitar without any electronics and goto: 1.
Those are very, very broad topics upon which entire books could (and likely have) been written, but in general professional guitarists go one of those three ways. Because good microphones are very expensive and can break easily, most live performances involve options 1 or 3--but some artists have been known to mike very old or expensive guitars that they didn't want to install electronics into. On to the questions.
What is a recording interface? A recording interface is an electronic device of some sort designed to take the signal generated by your instrument, run it through some transformations, and send it somewhere else for storage or more processing.
What is an Acoustic/Electric guitar? An Acoustic/Electric guitar is an Acoustic guitar that has a pickup installed in it. These come in many flavors.
How can I record a standard Acoustic guitar without a pickup? You can install a pickup in it or use a microphone positioned in front of the sound hole of the guitar. There are many methods to miking an acoustic guitar, but I won't get into those here.
How can I record using a microphone? In general this requires a gadget called an audio interface which hooks up to a computer, mixer, or other processing device. You run a cable from the microphone to one of the inputs on the audio interface, calibrate your software, start recording, and then start playing.
How can I record using an Acoustic/Electric guitar The same way you record using a microphone, except instead of plugging the microphone into the audio interface you plug the guitar in. Most audio interfaces support standard 1/4 inch jacks used by all Acoustic/Electric or electric guitars.
As you mention, the quality of the devices you use will affect how your guitar sounds. Higher quality components sound better, but are consequently more expensive. Hopefully that will answer some of the more basic facets of your question :).