Updated: Jun 23, 2018
There's a LOT of ways to record sound from analog tape decks to computerized systems, and they all have certain advantages. If you are on a budget and are setting up to record at home, allow me to toss a couple tips out here that will reap you huge rewards down the line as your skill level and gear acquisition syndrome (GAS) increases.
To get a recording to sound good, three things matter more than anything else.
Microphone, the room, and speakers.
It all starts here. Unless you're only recording synthesizers you need a mic. Always start with the best vocal mic you can afford. It's the lens on the camera. Good sounding mics are inspiring to sing through and will present your artistic vision in the best light. Big studios have really expensive mics for a reason! Microphone pre-amps matter a bunch too, but that's a whole other blog.
Your surroundings actually have a profound effect on the tone and depth of your recordings. A super dead room can leave you sounding dull, and a bright bouncy room can make your vocals hard to mix, cheap, and hard to understand. I recommend searching youtube for DIY videos on room treatment. Often the solution can be very affordable. You can edit a lot of things, but it's really hard to change the sound of a room on a recording---you're mostly stuck with it as you start to mix.
The last thing in your chain is listening back to what you have done and making critical decisions about your work. Get the best speakers you can afford! They matter.
If at all possible, listen to them first and make sure you enjoy how they sound. Then as you start mixing, get to know how they relate to other speakers. How much bass should I use? Positioning is critical too. An equilateral triangle between your head and the Left and Right are recommended. Get them away from the wall and supported by non-resonant stands. You can't make good sounding music without an accurate representation of what you have done.