Research and purchase a condenser microphone that is within your budget and has a history of successful reviews by people who've used it. A Behringer B-1, for example, is a staple in the voice-over industry, and can be purchase for under $100 if you look hard enough.
Condenser microphones use a vibrating chamber to record sound, making them responsive to something as delicate as the human voice. Dynamic microphones, while more rugged, don't pick up nearly as much sound as the condensers.
Attach your microphone to the mic stand of your choice; which mic stand you choose depends entirely on your style of recording. Some people prefer the musical microphone stand, whereas others would rather have a smaller, desk-seated stand.
Let your mic's cord be loose and movable, because you'll be using it here in a minute.
Obtain a simple preamp capable of both powering and boosting the signal from your condenser microphone. For example, the Behringer MIC 100, another staple in the recording industry, offers a full complement of sound-enhancing features, such as gain, limiter and a 20-decibel pad without swamping you in useless bells and whistles. Plug your mic's cord into the preamp's input channel.
Gain, simply put, makes your microphone's regular recording volume louder. A limiter keeps your voice from distorting while recording, and a pad stops the microphone from recording over a certain volume. For recording your voice, these are the three major features you'll want in your preamp.
Record your files into any simple audio program, as long as it's capable of recording files into MP3 format. Almost any computer should be able to run a simple recording program, as long as it has a microphone input jack somewhere on it.
Since you don't need extremely high-end sound effects or equalization features, a free recording tool, such as Audacity, should be more than adequate for your needs.
Set up all the aforementioned equipment in a relatively sound-proof environment. Since you're not producing extremely high-fidelity sound files, you don't need a completely noise-sterile sound booth. Just make sure that when you record you can't hear barking dogs, cars driving by or other noise pollution.
Listen to all of your recorded files through a set of small studio speakers to catch any missed noise pollution.