For most uses, digital recording on a home computer offers a powerful combination of quality and flexibility unmatched by analog methods. Some analog methods such as the four-track recorder, for example, are still useful for evoking a lo-fi, garage band feel that software might not be able to replicate without extra steps. Remember, if you record in an analog format and wish to edit your material digitally, you'll have to convert it in real time, effectively doubling the length of your recording session.
As a standalone alternative to a complex home recording setup, the Ovation iDea is an acoustic-electric guitar with an on-board digital recorder that captures your sessions in mp3 format. Consider an all-in-one option like the iDea with managed expectations, however, as your editing options are extremely limited.
Your next big decision is how to record. You can capture your acoustic guitar's sound by placing a microphone near the sound hole or by connecting an audio cable from an acoustic pickup directly into your recording equipment. You'll have to make a creative choice here, as each method records different aspects of your guitar.
A microphone will not only capture the guitar string's vibrations, but also ambient textures including physical contact along the strings and guitar body, as well as the guitar's echo within your recording space. You'll have the flexibility to position the microphone at different points along the sound hole, producing progressively brighter tones as you place the mic along the neck. For a fuller, stereo sound, experiment with two microphones---one placed near the center of the sound hole and the other placed along the guitar neck.
Recording straight into your recording equipment requires an acoustic pickup, which you can add to your guitar as a removable sensor bar inserted across the sound hole or a permanent fixture installed into the guitar body. No matter what pickup you use, you'll get a cleaner audio signal and can avoid unwanted background noise from your recording space. Although microphones generally achieve higher quality recordings, you can always record using both methods simultaneously and mix them together to achieve a full range of sound.
If you're recording a song with familiar structures like an intro, verse or chorus, consider recording each section as a loop. A loop is a short musical phrase you can record once, then repeat indefinitely to create your full-length track. The key quality of loop recording is consistency. Using digital editing software, you can create multiple loops, then repeat and arrange them to construct your song from a collection of mistake-free building blocks. This level of consistency might not be appropriate for all musical styles, however, especially if you want to incorporate subtle variations throughout your chord progressions.
No matter how well you know your material, always perform multiple takes. This is especially important if you're recording by yourself. Upon playback, you'll hear your sound from a listener's perspective, which could reveal slight mistakes or imperfections you need to fix. With multiple takes to work with, you'll also have the option of mixing and matching sections from all your takes to create the best track.