"Quality" is a big range. For example, you aren't going to get a professional, radio quality sound without having the equipment they use in professional recording studios. And, surprise surprise, it costs a whole lot of money.
However, demo/good home recording/great quality is not as expensive.
You're gonna need an interface to go from microphone to computer. You're gonna need a good microphone, specifically one that sounds good on your voice. More importantly, though, you're gonna need some knowledge. You can get some great sounding vocal tracks with as little as $100 worth of equipment. It's all in knowing how to use what you've got.
This website is a great resource for the general theory behind acoustic treatment:
http://www.ethanwiner.com/acoustics.html
This website has some great tutorials on the theory behind two really important skills that you'll end up needing - gain staging and proper use of compression:
http://www.independentrecording.net/irn/
No website is springing to mind on the theory behind recording vocals, but there is a wealth of information out there and on this very site that can get you going in the right direction.
Interface-wise, if you're only ever recording vocals, you could get away with a single channel usb interface that has a mic preamp in it - check out the lexicon alpha:
http://www.sweetwater.com/store/detail/Alpha/?gclid=CK3AuP2zpJ4CFRDFsgodegiQlg
It's pretty inexpensive, was my first interface, and worked really well for me.
As far as mics go, it's gonna be really tough for anyone to tell you what works for you. Just go to the mic forum and find one of the numerous threads on "best vocal mic." There are as many answers as there are people answering. One thing to do might be, if you've ever recorded vox in a studio before and really liked the sound of them, try and get in touch with them and figure out which mic they used on you. Ultimately it's gonna take a lot of trial and error, so you might want to buy an inexpensive mic, do some simple recordings, and figure out what you do and don't like about your recorded voice. Then, go to your local music mega store and try out some of their mics. Once you've heard what you are and aren't liking from the cheapo mic, you'll be better able to hear what the ones you are trying out do for your voice.
Like I said, trial and error is gonna play a big part. Definitely don't expect to buy the right equipment, set it up, and have it give you perfect sound right away. Recording is as much an art as singing, and takes as much work, skill and talent (more if you're one of those naturally gifted singers) to do it well.
Good luck, and have fun.
